DEEPAK SIR LIGHT

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1 LIGHT Before the beginning of the nineteenth century, light was considered to be a stream of particles (called corpuscles). Newton used this corpuscular theory to explain reflection and refraction of light. In 1678, a Dutch physicist, Christian Huygens ( ) proposed that the light was wave-like in character. The wave theory of light was not accepted immediately. The wave-like character of light was experimentally proved in 1801 by Thomas Young ( ). Maxwell in 1873 proposed that light was a form of high frequency electromagnetic wave. Hertz confirmed the Maxwell's theory experimentally in By this time, the wave theory of light seemed to be on firm ground. However, in the beginning of the twentieth century, Max Planck (1901) used corpuscular theory to explain the radiations emitted by hot objects. Albert Einstein used corpuscular theory to explain the photoelectric effect in What is light Light is a form of energy that we can detect with our eyes. We can define light as follows also. Light is a form of energy which enables us to see objects which emit or reflect light. We get light from various sources, e.g. sun, electric lamp, candle, and an oil lamp, etc. The objects which emit (give) light are called luminous objects. Luminous objects may be natural or man-made. Sun is a natural source of. light. Stars also emit light. An electric lamp, and an oil lamp, etc. are man-made sources of light. The non-luminous objects do not emit light. However, such objects become visible due to the reflection of the light falling on them. Moon does not emit light. It becomes visible due to the reflection of the sunlight falling on it. What are the characteristics of light Some common characteristics of light are given below: (i) Light is an electromagnetic wave. (ii) Light is a transverse wave, and does not need any medium to travel. Light can travel through vacuum. Its speed through vacuum is 3 x 10 8 m/s. (iii) The velocity of light changes when it travels from one medium to another.wavelength (λ) of light changes when it goes from one medium to another. The frequency (v) of the light wave remains the same in all media. (iv) Light can pass through transparent materials, such as glass or air. However, it cannot pass through opaque materials, such as wood, metals, etc. Light can pass through translucent materials, such as waxed-paper, frosted glass etc. only partially. (v) Light travels in a straight line. (vi) Light gets reflected back from polished surfaces, such as mirrors, polished metal surfaces, etc. (vii) Light undergoes refraction (bending) when it travels from one transparent medium to another. Today, scientists view light as having dual nature: sometimes behaving like a particle and sometimes like a wave. The particulate nature of light is shown by the photoelectric effect, whereas the phenomena of reflection and refraction show that the light behaves like a wave. ray of light Beam of light What is meant by a ray and a beam of light A straight line drawn in the direction of propagation of light is called a ray of light. A ray is described by a straight line with an arrow-head pointing in the direction of propagation of light. A bundle of the adjacent light rays is called a beam of light. A beam of light can be Parallel beam of light Convergent beam of light Divergent beam of light The beam of light in which all the rays are parallel to each other is called parallel beam of light. A beam of light coming from a distant source (such as, the sun) is called a parallel beam of light. The beam of light in which the rays of light starting from a point source move out in different directions is called a divergent beam of light. The beam of light coming out of a flashlight is a divergent beam of light. The beam of light in which the rays of light starring from a large source of light get closer to each other (or move towards a point) is called convergent ray of light. REFLECTION OF LIGHT What is meant by reflection of light When a ray of light falls on a polished smooth surface, such as a mirror, it returns back into the same medium. This is called reflection of light. Different materials reflect light to different extent. Silver is one of the best reflectors of light. We see our images in a mirror due to reflection of light. The ray of light which falls on a polished surface (or a mirror) is called the incident ray of light. The ray of light which gets reflected from a polished surface (or a mirror) is called the reflected ray of light. The normal is a line at right angle to the reflecting surface, such as, a plane mirror, at the point of incidence. The angle made by the incident ray with the normal is called the angle of incidence ( i). The angle made by the reflected ray with the normal is called the angle of reflection ( r). The incident ray, the reflected ray, the normal and the angles of incidence and reflection are shown 1 P a g e

2 Regular or specular reflection Irregular reflection Kinds of reflection Depending on the nature of the reflecting surface, there could be two kinds of reflections. Regular (or specular) reflection Irregular (or diffused) reflection The reflection of light from a mirror-like smooth reflecting surface so that the reflected rays are parallel to each other is called regular or specular reflection The reflection of light from a rough, irregular surface randomly in various directions (not parallel to each other) is called irregular or diffused reflection What are the laws of reflection Reflection of light from a smooth surface follows the following two laws of reflection. These laws of reflection are true for all kinds of mirrors, i.e., for plane mirror as well as spherical mirrors (concave and convex mirrors). Law 1. The angle made by the incident ray with the normal at that point is equal to the angle made by the reflected ray with the normal, i.e. Angle of incidence = Angle of reflection or i = r Law 2. The incident ray, the reflected ray and the normal at the point of incidence, all lie in the same plane. What happens to a ray of light that falls on a mirror normally (or at right angle) When a ray of light falls on a mirror normally (along the normal), i.e., at right angle, the incident ray coincides with the normal. Therefore, That is, the reflected ray will also travel along the normal. Thus, when a ray of light falls on a mirror normally or at right angle, it gets reflected back along the same path. Home work 1. What is light? 2. Name some common sources of light. 3. What is the speed of light in vacuum? 4. Write down three characteristics of light. 5. Name two natural phenomena based on the property that light travels in straight lines. 6. State the laws of reflection 7. The angle between an incident ray and the mirror is 30. (a) What is the angle of incidence? (b) What is the angle of reflection? (c) What is the total angle turned by the ray of light? MIRRORS What is a mirror A smooth, highly polished reflecting surface is called a mirror. Commonly used mirror (looking glass) is made by depositing a thin layer of silver metal on one side of a plane glass sheet. The silver metal layer is then protected by a coating of red lead oxide paint. In all kinds of mirrors, silver layer acts as the reflecting surface. There are two types of mirrors: (a) Plane mirror. A highly polished plane surface is called a plane mirror. (b) Curved mirror. In curved mirrors, the reflecting surface is curved. The curved mirrors are called spherical mirrors or parabolic mirrors depending upon their curvature. A plane mirror, a spherical mirror and a parabolic mirror are shown alongsideat this level, we would describe only plane and spherical mirrors. What are spherical mirrors A mirror whose polished, reflecting surface is a part of a hollow sphere of glass (or plastic) is called a spherical mirror. For a spherical mirror, one of the two curved surfaces is coated with a thin layer of silver followed by a coating of red lead oxide paint. Thus, one side of the spherical mirror is made opaque, and the other side acts as a reflecting surface. The opaque side of a mirror is shown shaded 2 P a g e

3 Depending upon nature of the reflecting surface of a mirror, the spherical mirrors may be classified as concave mirror and convex mirror. (a) Concave mirror. A spherical mirror whose inner hollow surface is the reflecting surface is called a concave mirror. (b) Convex mirror. A spherical mirror whose outer bulging out surface is the reflecting surface is called a convex mirror. TERMINOLOGY FOR SPHERICAL MIRRORS When we describe the formation of images by spherical mirrors we use many terms. Each of these terms has a specific meaning. So, before describing the formation of images by spherical mirrors, we describe these terms. What are the various terms associated with a spherical mirror The following terms are often used during the description of spherical mirrors: (a) Aperture (b) Pole (c) Centre of curvature (d) Radius of curvature (e) Principal axis (f) Normal (g) Focus (or focal point) (h) Focal length (i) Focal plane (j) Real image (k) Virtual image Some of these terms are described below (a) Aperture. The effective width of a spherical mirror from which reflection can take place is called its aperture. In Fig. 1.8, the distance MM' is the aperture of the spherical mirror. (b) Pole. The centre of a spherical mirror is called its pole. This point is taken as the reference point for measuring the distances of object and image from the mirror. The pole of a mirror is denoted by P (Fig. 1.8). (c) Centre of curvature. The centre of the hollow sphere of which the spherical mirror is a part is called centre of curvature of the spherical mirror. The centre of curvature of a spherical mirror is denoted by C (Fig. 1.8). (d) Radius of curvature. The radius of the hollow sphere of which the spherical mirror is a part is called the radius of curvature (R) of the spherical mirror. From the Fig. 1.8, the distance PC is the radius of curvature of the spherical mirror. (e) Principal axis. The straight line passing through the centre of curvature and the pole of a spherical mirror is called its principal axis. In Fig., the line xy passing through the centre of curvature (C) and the pole (P) is the principal axis of the spherical mirror. (f) Normal. The normal at any point of the spherical mirror is the straight line obtained by joining that point with the centre of curvature of the mirror. The normal at point A on the mirror is the line AC obtained by joining the point A to the centre of curvature of the mirror (Fig.. Normal at any point on a spherical mirror is equal to the radius of the sphere of which the mirror is a part. (g) Focus (or focal point). The point on the principal axis where all the rays coming from infinity (parallel rays) after reflection either meet or appear to meet is called the focus (or focal point) of the mirror. Focus of a concave mirror. The focus of a concave mirror is a point on its principal axis at which all the rays coming from infinity (parallel rays) converge (meet) after reflection from it. In Fig. 1.10a, point F is the focal point or focus of the concave mirror. (i) The focus of a concave mirror is in front of the mirror. (ii) The focus of a concave mirror is a real focus, because the light rays after reflection from a concave mirror actually converge at the focus (point F). This is why a concave mirror is also called a converging mirror. Focus of a convex mirror. The focus of a convex mirror is a point on its principal axis from where the reflected rays appear to diverge after a parallel beam of light is reflected from the convex mirror. Fig the point F is the focus (or focal point) of a convex mirror. (i) The focus of a convex mirror lies behind the mirror. (ii') The focus of a convex mirror is a virtual focus, because the incident rays after reflection from a convex mirror appear to come from the focus (point F). In a convex mirror the reflected rays diverge after reflection. So, a convex mirror is also called a diverging mirror. h) Focal length. The distance between the pole (P) and the focus (F) is called focal length (f). Thus, in Fig. 1.10, the distance PF is equal to the focal length of a spherical mirror. Focal length (f) of a spherical mirror =Radius of curvature (R)/ 2 (i) Focal plane. An imaginary plane passing through the focus and at right angles to the principal axis is called the focal plane of a mirror. (j) Real image. When the rays of light after getting reflected from a mirror (or after getting refracted from a lens - see next chapter) actually meet at a point, a real image is formed. A real image can be obtained on a screen. So, the image which can be obtained on a screen is called a real image. A concave mirror (or a convex lens) gives a real image if the object is placed at or beyond focus. (k) Virtual image. When the rays of light after getting reflected from a mirror (or after getting refracted from a lens - see next chapter) appear to meet at a point, a virtual image is formed. Such an image can only be seen through a mirror (or a lens) but cannot be obtained on a screen. So, the image which can be seen only in a mirror (or lens), but cannot be obtained on a screen is called a virtual image. For example, the images formed in a plane mirror are virtual images. A concave mirror (or a convex lens) forms a virtual image when the object is placed at distances less than the focal length. 3 P a g e

4 Real image A real image is formed when two or more reflected rays intersect each other at a point in front of a mirror. A real image can be obtained on a screen. Real images are inverted (upside down) with respect to the object. Virtual image A virtual image is formed when two or more reflected rays appear to intersect at a point behind a mirror. A virtual image cannot be obtained on a screen. It can only be seen in the mirror, j Virtual images are erect with respect to the i object. FORMATION OF IMAGES BY A PLANE MIRROR A plane mirror is a highly polished flat surface which reflects almost all the light falling on it. The following rays are usually used to construct ray diagrams for the formation of images by a plane mirror. (i) A ray of light falling on a plane mirror at 90 (perpendicular) gets reflected back from the mirror by the same path. (ii) A ray of light falling on a plane mirror at any angle gets reflected from the mirror such that the angle of incidence is equal to the angle of reflection.let us now draw a ray diagram to show the formation of an image by a plane mirror. The image in a plane mirror is (i) virtual, (ii) of the same size as the object, (iii) laterally inverted, and (iv) as far behind the mirror as the object is in front. The line joining the object to the image is at right angles (90 ) to the plane mirror. EXAMPLE For a plane mirror magnification M = +1. What does this signify for (a) M = 1, and (b) positive sign of M? SOLUTION, (a) The quantity, M = 1 signifies that the image formed in a plane mirror is of the same size as the object. (b) Positive sign in the value of magnification (M = +1), signifies that the image formed by a plane mirror is erect. Home work 1. What do you understand by the term mirror? How many types of mirrors are there? 2. Describe a plane mirror. 3. Describe a spherical mirror. 4. What is the focal length of a plane mirror? 5. Define focal length and radius of curvature for a spherical mirror. 6. What is the relationship between the focal length and radius of curvature in the case of a concave mirror? 7. If the radius of curvature of a concave mirror is 36 cm, what is its focal length? [Ans. 18 cm] 8. Define the focus (or focal point) and the focal length of a convex mirror. 9. What are real and virtual images? 10. A boy with a mouth 5 cm wide stands 2 m from a plane mirror. Where is his image and how wide is the image of his mouth? 11. Write a few letters (in capital) which do not show lateral inversion when placed before a plane mirror. FORMATION OF IMAGES BY A CONCAVE MIRROR When an object is placed in front of a concave mirror, light rays from the object fall on the mirror and get reflected. The reflected rays produce an image at a point where they intersect or appear to intersect each other. Formation of an image by mirrors (and lenses) is usually shown by a ray diagram. To construct a ray diagram, we need at least two rays whose paths after reflection from the mirror are known. So, before describing the ray diagrams, we describe the rays which can be used for constructing the ray diagrams. Which rays can be used to locate the image formed by a concave mirror? The following rays coming from the object are usually used to construct ray diagrams for locating the image formed by a concave mirror: (i) A ray of light travelling parallel to the principal axis after reflection from a concave mirror passes through its focus (F). This is shown in Fig.a. (ii) A ray of light passing through the focus (F) of a concave mirror after reflection goes parallel to the principal axis. This is shown in Fig. b. (iii) A ray of light passing through the centre of curvature (C) of a concave mirror returns back along the same path after reflection. This is because the ray passing through the centre of curvature strikes the mirror at 90. This is shown in Fig c. (iv) A ray of light falling on a concave mirror at its pole (P) gets reflected according to the law of reflection, i.e. angle of incidence is equal to the angle of reflection. 4 P a g e

5 What are the uses of a concave mirror The use of a concave mirror depends upon the distance of the object from the mirror. Some main uses of concave mirrors are given below: (i) Concave mirrors are used as reflectors in the headlights of cars, searchlights, etc. (ii) Concave mirrors are used by dentists (as the dentists' mirror) to focus light on the tooth to be examined. (iii) Concave mirrors are used as shaving mirrors and as make-up mirrors to see the enlarged erect image of the face. For this to happen, face must be placed closer to the mirror. (iv) Concave mirrors (or parabolic mirrors) are used as radiation collector in solar heating devices. Home work 1. Explain with a suitable diagram how does a concave mirror converge a parallel beam of light rays? 2. Define and show on a neat diagram the following terms for a concave mirror: (i) pole (if) aperture (Hi) radius of curvature (iv) principal axis (v) principal focus. 3. For which position of an object, a concave mirror forms a real image equal in size to the object? 4. For which position of the object does a concave mirror produce an inverted, magnified, real image. 5. For what position of an object, a concave mirror forms an enlarged virtual image? 6. The image formed by a concave mirror is seen to be virtual, erect and larger than the object. What is the position of the object? 7. One wants to see an enlarged image of an object in a mirror. What kind of mirror should one use and where should the object be placed? 8. Name the spherical mirror which can produce a real and diminished image of the object. 9. Where should an object be placed in front of a concave mirror so as to obtain its magnified erect image? Numerical Problems: Draw a suitable ray diagram where necessary. 1. An object is placed 20 cm in front of a concave mirror of focal length 12 cm. Find position and nature of the image. [. v = -30 cm, real, inverted] 2. Describe the nature of an image formed when an object is placed at a distance of 20 cm from a concave mirror of focal length 10 cm. [Ans. real, inverted, same size image at 20 cm from the mirror] 3. If an object is placed at a distance of 8 cm from a concave mirror of focal length 10 cm, discuss the nature of the image formed by drawing the ray diagram. [Ans. virtual, erect, enlarged, v= 40 cm] 4. What is the position of the image when an object is placed at a distance of 20 cm from a concave mirror of focal length 20 cm? [Ans. infinity] 5. Find the size, nature, and position of the image formed when an object of 1 cm size is placed at a distance of 15 cm from a concave mirror of focal length 10 cm. [Ans. v= -30 cm, real, inverted, 2 cm in size] 5 P a g e

6 In all these cases, the ray parallel to the principal axis after reflection appears to come from the focus (F) behind the mirror. Another ray going towards the centre of curvature (C) behind the mirror gets reflected by the same path. The two reflected rays appear to intersect at a point between F and P behind the mirror. So, the image appears to be formed behind the mirror. In all these cases, the image is virtual, erect and smaller than the object. Thus, we see that "for a convex mirror, the image formed is always virtual, erect and smaller than the object whatever may be the position of the object in front of the What are the uses of a convex mirror Convex mirrors are often used as, (i) rear-view mirrors or side-minor (also called drivers minor) on automobiles, such.is cars, trucks and buses to see the traffic coming from behind. (ii) staircase-mirrors on the double-decker buses. (iii) vigilance-mirrors in big shops and stores. Why is a convex mirror preferred for its use as a driver's mirror A convex mirror is preferred to be used as a driver's mirror (rear-view mirror) because of the following reasons: (i) a convex mirror always forms an erect (right side up) image of an object whatever may be its distance from the mirror. This makes identification of the object coming from behind easy. (ii) a convex mirror forms an image which is much smaller than the object. As a result, images of a large number of objects coming from behind can be seen in the mirror at the same time. Because of this, a convex mirror has a wider field of view. How to distinguish between a plane mirror, a concave mirror and a convex mirror without touching them Bring each mirror one by one closer to your face, and observe the image formed in the mirror. Then, (i) if the image is equal in size, and erect, it is a plane mirror, (ii) if the image is large and erect, it is a concave mirror, (Hi) if the image is smaller and erect, it is a convex mirror. EXAMPLE. The image formed by a concave mirror is observed to be virtual, erect and larger than the object. Then, the position of the object should be (i) between the focus and the centre of curvature (ii) at the centre of curvature (iii) beyond the centre of curvature (iv) between the pole of the mirror and its focus. SOLUTION. The correct answer is (iv), i.e., the object should be placed between the pole and the focus of the mirror. EXAMPLE No matter how far yon stand from a spherical mirror, your image appears erect. The mirror may be (i) plane (ii) concave (iii) convex (iv) either plane or convex SOLUTION. The correct answer is (iii). A convex mirror always forms a virtual, erect image, whatever may be the position of the object. SIGN CONVENTION FOR REFLECTION BY SPHERICAL MIRRORS What is the sign convention for spherical mirrors The following sign conventions, called the New Cartesian Sign Convention, are used for measuring various distances in the ray diagrams of spherical mirrer i)the pole of the mirror is taken as the origin. Thus, all distances are measured from the pole of the mirror. (ii) The object is placed on the left of the mirror. Thus, the incident ray is considered to travel from left to right, (iii) Distances measured in the direction of the incident ray i.e., right of the pole are taken as positive. (iv) Distances measured in the direction opposite to that of the incident rays i.e., left of the pole are taken as negative. (v) Distances measured above the principal axis are positive, e.g. height of an object and of an erect image are positive. (vi) Distances measured below the principal axis are negative, e.g. height of a real inverted image is negative. 6 P a g e

7 MIRROR FORMULA What is mirror formula The relationship between distance of the object (u), distance of the image (v) and focal length (f) of a spherical mirror is called mirror formula. Mirror formula is written as, OR This relationship is applicable to both the concave and convex mirrors. The mirror formula contains three terms. If any two are known, the third can be obtained from it. So, the mirror formula is often used in numerical problems. While using the mirror formula, the following rules must be followed: (i) The values of the known parameters should be used with their proper signs as per sign convention, (ii) No sign should be attached to the unknown parameter during calculations. Its sign will come of its own after calculations. How is the focal length of a concave mirror determined Parallel rays (the rays coming from a far-off object) after reflection from a concave mirror meet at its focus (F). This property of a concave mirror can be used to determine its focal length. There are many methods for determining the focal length of a concave mirror. Here, a very simple method (although not very accurate) is described. Hold a concave mirror facing any distant object, such as a tree or a building. Place a screen (or a thick white paper) in front of the mirror. Focus the image of the object on the screen to obtain the sharpest image of the object. Then, measure the distance between the screen and the pole (P) of the mirror. This distance is equal to the focal length of the concave mirror. What is meant by magnification produced by a mirror The ratio of the size (height) of the image to the size (height) of the object is called magnification or lateral magnification. Magnification is denoted by M. Thus, magnification produced by a mirror, For all mirrors, the height of object (ho) is always positive, while the height of image (h1) may be negative or positive. So, the magnification produced by a mirror may be negative or positive. When the height of image (h1) is negative, magnification is negative, and when the height of image (h1) is positive, magnification is positive. For an inverted image. As per sign convention, the height of image (h1 ) for an inverted image is negative. So, the magnification of a mirror is negative when it produces an inverted image. Therefore, if the magnification of a mirror is negative, then the image produced by the mirror is inverted and real (because real images are inverted in the case of mirrors). For an erect image. For an erect image, the height of image (h1) is positive. So, the magnification of a mirror is positive when it produces an erect image. Therefore, if the magnification of a mirror is positive, then the image produced by the mirror is erect and virtual (because all virtual images formed by a mirror are erect). EXAMPLE. The radius of curvature of a convex mirror used on a moving automobile is 2.0 m. A truck is coming behind it at a constant distance of 3.5 m. Calculate (i) the position, and (ii) the size of image relative to the size of the truck. What will be the nature of the image? 7 P a g e

8 EXAMPLE. An object is placed at a distance of 10 cm from a convex mirror of focal length 15 cm. Find position and nature of the image. What is meant by refraction of light Light travels in straight line through any medium of uniform density. However, when a ray of light travels from one transparent medium to another (say, from air to glass), it suffers a change in its direction. This bending of a ray of light as it passes from one medium to another is called refraction. The direction in which the ray of light bends when it travels from one medium to another depends upon the optical density of the two media. When a ray of light travels from an optically rarer medium to an optically denser medium, it bends towards the normal. That is Angle of refraction (Zr) < Angle of incidence (Zi) When a ray of light travels from an optically denser medium to an optically rarer medium, it bends away from the normal. That is Angle of refraction (Zr) > Angle of incidence (Zi) Air is optically less denser than water or glass. Therefore A ray of light travelling from air into glass bends (or refracts) towards the normal. A ray of light travelling from glass into air bends (or refracts) away from the normal. What are the laws of refraction The two laws of refraction are Law 1. The ratio of sine of the angle of incidence to the sine of the angle of refraction for a particular pair of media is constant. Thus, if the angle of incidence is i, and that of refraction is r, then Law 2. The incident ray, the refracted ray and the normal at the point of incidence, all lie in the same plane. What is the cause of refraction of light The speed of light depends on the nature of the medium in which it travels. When light travels from a rarer medium to a denser medium, its speed decreases. Whereas speed of light increases when it travels from a denser to a rarer medium. It is due to this change in the speed of light that the ray of light bends as it goes from one medium to another. Thus, the change of speed of light as it travels from one medium to another is the cause of refraction. Snell's law and the refractive index of the medium Let us consider a rav of light travelling from a medium. Then, from Snell's law 8 P a g e

9 As a light wave moves from medium I to medium 2, its wavelength changes, but its frequency remains the same. Wavelength of light wave decreases when it enters a denser medium from a rarer medium side, e.g. from air to glass. As a result, the speed of light decreases when it enters a denser medium from a rarer medium side. Diamond has the highest optical density, Air has the lowest optical density. When two transparent media are compared, the one with higher refractive index is termed optically denser (or denser) whereas the other one having lower refractive index is termed optically rarer (or rarer) medium. Does refractive index of a medium depend on the wavelength of light? The refractive index of any medium depends upon the wavelength of light used in its measurement. Experimentally, it has been seen that the refractive index of any material decreases with increase in the wavelength of light. In visible spectrum, the wavelength decreases as we go from red to violet. Therefore, the refractive index of a material for violet light is greater than that for red light. That is why, all refractive-index values are measured using the yellow light (sodium light) of 589 nm. How is the speed of light in a medium related to its refractive index The refractive index of a medium is related to the speed of light in that medium through the relationship, Refractive index of a medium, n = Speed of light in vacuum (c)/speed of light in the medium (v) Speed of light in water > Speed of light in glass (crown) > Speed of light in diamond REFRACTION OF LIGHT THROUGH A GLASS SLAB Refraction of light through a glass slab can be studied as follows: ACTIVITY: To verify the laws of refraction and determine the refractive index of the glass Materials required: Rectangular glass slab, White sheet of drawing paper, Drawing board, Drawing pins and all-purpose pins (pins) Procedure: Fix a plain sheet of paper on a drawing board with the help of drawing pins. Place a rectangular glass slab in the middle of the paper and draw its boundary with a sharp pencil. Fix two pins (P, and P2) vertically along a straight line AB. Now look through the glass slab from the other side and fix two pins (P3 and P4) so that those pins and the images of the pins P, and P2 are in a straight line (when seen through the glass slab). Remove the glass slab and all the pins. Mark the positions of the pins. Join the points P, and P2 and extend the line to meet one face of the slab (Point B). Similarly, extend the line obtained by joining the points P3 and P4 to meet the other face of the slab (point C). Also join the points B and C. Draw perpendiculars to the two faces of the slab at point B and point C. Measure and record the angle of incidence (i) and the angle of refraction (r). Repeat the experiment for different angles of incidence and determine the corresponding angles of refraction. Calculations: (i) Calculate the ratio sin i I sin r for all the observations. Calculate the average of all these values. Results: From the calculations, following results are obtained: (i) The ratio sin / / sin r for all observations is constant. (ii) The plot of sin i vs sin r is a straight line passing through the origin. The slope of sin I vs sin r plot is equal to the ratio sin i I sin r. Conclusions: (i) The constant value of the ratio sin i I sin r and the straight line plot between sin i and sin r verify the first law of refraction or Snell's law. (ii) The incident ray, refracted ray and the normal, all lie in the same plane, i.e. plane of the paper. This verifies the second law of refraction. (iii) The average value of the sin / / sin r ratio is equal to the refractive index of the glass of the slab. (iv) The slope of sin i vs sin r plot is equal to the refractive index of the glass of the slab. Prove that for refraction through a rectangular glass slab, the emergent ray is parallel to the incident ray Let us consider the refraction of a ray of light (AB) through a glass slab as shown in Fig. Then for refraction at point B, i.e., the angle of emergence is equal to the angle of incidence. Thus, the emergent ray CD is parallel to the incident ray AB. What is meant by lateral displacement While studying refraction through a glass slab, it is seen that the emergent ray of light is parallel to the incident ray but laterally displaced from the path of the incident ray. The perpendicular distance of separation between the emergent ray and the original path of the incident ray is called lateral displacement. Lateral displacement of the emergent ray of light increases with an increase in the thickness of the medium <> an increase in the angle of incidence an increase in the refractive index of the medium a decrease in the wavelength of light Thus, for the same slab and the same angle of incidence, the lateral displacement will be more for violet light than the red light. 9 P a g e

10 What is meant by the reversibility of light When the final path of a ray of light after any number of reflections and refractions is reversed, the ray of light retraces back its entire path. This is called the principle of the reversibility of light. Q.l. You arc given kerosene, turpentine and water. In which of these does the light travel fastest?. Ans. The refractive index values of the three liquids are Kerosene Turpentine Water We know from the definition of refractive index, that the speed of light is higher in a medium with lower-refractive index. So, the light travels fastest in water. Q.2. The refractive index of diamond is What is the meaning of this statement? Ans. This statement means that the speed of light in diamond is lower by a factor of 2.42 relative to that in vacuum. Home work 1. Draw a diagram showing the bending of a ray of light when it travels from a rarer medium to a denser medium. 2. What happens when a ray of light strikes the surface of separation between the two media at right angle? 3. Write the mathematical equation describing Snell's law. 4. In which of the following three media, the speed of light is (a) the highest, (/>) the lowest? Water, Glass, Diamond 5. Draw a diagram showing refraction of light through a glass slab. REFRACTION BY SPHERICAL LENSES ( Deepak sir ) Lenses are used to form images by refraction in optical instruments, such as cameras, telescopes, and microscopes. In fact, even at this moment you are using the lenses in your eyes to read these words. There is a variety of lenses but here, we will describe lenses of the simplest forms only. A convex lens is also called a converging lens, and a concave lens is also called a divergent lens. Deepak sir TERMINOLOGY FOR LENSES When we describe the formation of images by lenses, we use many terms. Each of these terms has a specific meaning. So, before describing the formation of images by lenses, we describe these terms. What are the various terms associated with a lens The following terms are often used during the description of lenses: (a) Aperture (b) Optical centre (c) Principal axis (d) Focus (or principal focus) (e) Focal length (f) Focal plane (g) Power These are shown in Fig., and described below: (a) Aperture. The effective width of a lens from which refraction takes place is called its aperture. In Fig., the distance LL' is the aperture of the lens. (b) Optical centre. The centre point of a lens is called its optical centre. It is denoted by the letter O. In the case of lenses, all the distances are measured from the optical centre. A ray of light passing through the optical centre of a lens does not suffer any deviation. (c) Principal axis. Principal axis is also called optical axis of the lens. The line passing through the optical centre of the lens and perpendicular to both the faces of the lense (d) Focus (or principal focus). A point on the principal axis at which parallel rays of light after passing through a lens converge or appear to diverge from it is called its principal focus, or simply as focus. 10 P a g e

11 Focus of a convex lens. The focus of a convex lens is a point on its principal axis at which all the rays coming from irifiriity (parallel rays) converge after passing through the lens. In Fig., the point F is the focus of the convex lens. Focus of a concave lens. The focus of a concave lens is a point on its principal axis from which all the rays coming from infinity (parallel rays) appear to diverge after passing through the lens. In Fig., the point F is the focus of the concave lens. (e) Focal length. The distance between the focus and the optical centre of a lens is called its focal length. Focal length of a lens is denoted by f. In Figs, the distance FO is called the focal length of the lens. (f) Focal plane. An imaginary plane perpendicular to the principal axis and passing through the focus of a lens is called its focal plane. (g) Power of a lens. The reciprocal of the focal length of a lens measured in metres is called its power. Power of a lens is denoted by P. So, Power of a lens, P = 1 / focal length in meter { Power of a lens is measured in dioptre unit (1 D = I m -1 )} THE IMAGES FORMED BY A CONVEX LENS The following rays coming from the object are usually used for constructing ray diagrams for images produced by a convex lens: (1) A ray of light coming parallel to the principal axis after passing through a convex lens passes through its focus (2) A ray of light passing through the optical centre of the lens travels straight without suffering any deviation. This, however, is true only for a thin lens because the two sides of a lens at its centre are parallel only when the lens is thin. (3) A ray of light coming from an object through the focus of a convex lens becomes parallel to its principal axis after passing through the lens. object at infinity, a convex lens forms an inverted, real and highly diminished image at the focus (F) object is placed beyond 2F, an inverted, real image is formed between F and 2F on the other side of the lens. object is placed at 2F from a convex lens, an inverted, real image of the same size as the object is formed at 2F on the other side of the lens. When an object is placed between F and 2F, an inverted, real and enlarged image is formed beyond 2F on the other side of the object is placed at F, its inverted, real and highly magnified image is formed at infinity. object is placed between F and 0 before a convex lens, a virtual, erect, and enlarged image of the object is formed on the same side of the lens as the object. The diagram (last) explains the use of a convex lens as a magnifying glass or as a simple microscope. What are the uses of a convex lens Convex lenses are converging lenses. These are mainly used (i) as magnifying glass (ii) in spectacles (iii) as objective and eye-pieces in many instruments, such as telescopes and microscopes (iv) as a lens in cameras and projectors (v) in theatre spotlights 11 P a g e

12 Q. We wish to obtain a real, inverted image of the same size as that of the object by a thin convex lens of focal length 20 cm. Where should the object be placed? Draw the ray diagram to show the image formation in this case. Home work 1. What is a lens? How many types of lenses are there? 2. Describe (a) a convex lens, (b) a concave lens. 3. What is a lens? Distinguish between a convex and a concave lens. 4. Why is a convex lens called a converging lens? Explain with the help of a diagram. 5. Explain with the help of a diagram, why is a concave lens called a divergent lens? 6. A thin lens has a focal length, f = -12 cm. Is it a convex or a concave lens? 7. If the image formed by a lens is always diminished and erect then what is the nature of the lens? [Ant. concave] 8. For what position of an object, a virtual image is formed by a convex lens? (Ant. lass than f 9. Where should an object be placed so that a real and inverted image of the same size is obtained using a convex lens? [Ans. at 2f ] 10. If the image formed by a convex lens is of the same size as that of the object, then what is the position of the image with respect to the lens [. at 2f] 11. A 1 cm high object is placed at a distance of 2 f from a convex lens. What is the height of the image formed?( [Ans. - 1 cm, Negative sign means the image is inverted] Numerical Problems: 1. Find the position, size and nature of the image of an object 5 cm high which is placed 10 cm in front of a convex lens of focal length 6 cm. [Ans. v= 15 cm; real, inverted, magnified; 7.5 cm high] 2. Find the position and nature of an image formed by a convex lens of focal length 15 cm when an object 6 cm high is placed 30 cm in front of the lens. [Ans. v = 30 cm; real, inverted, and same size] 3. The lens of a camera has a focal length of 10 cm. What must be the distance between the lens and the film in order to photograph objects at (a) infinity (b) 20 cm from the lens. [Ans. (a) 10 cm, (b) 20 cm] 4. An object 4 cm high is placed 15 cm from a convex lens of focal length 5 cm. Draw a ray diagram on graph paper (full size or 1/2 scale) and find the position, size and nature of the image. [Ans. v = 7.5 cm; 2 cm; real, inverted] FORMATION OF IMAGES BY A CONCAVE LENS A concave lens always gives a virtual, erect and diminished image of an object, whatever may be the distance of the object from the lens. As a result, concave lenses do not find many uses. Concave lenses are used mainly in spectacles for the correction of shortsightedness DEEPAK SIR What is the sign convention for lenses LENS FORMULA Lens formula is also called lens equation. The relationship between distance of the object (w), distance of the image (v) and focal length if) of the lens is called lens formula or lens equation. Lens formula is written as, /f =1/v -- 1/u Focal length of the lens Distance of the image from Distance of the object the lens from the lens where, f is the focal length of the lens u is the distance of the object from the optical centre of the lens v is the distance of the image from the optical centre of the lens Equation or lens formula, and it is applicable to both convex andconcave lenses. While using this formula the following rules must be followed: 12 P a g e

13 The values of the known parameters should be used with their proper sign (- or +) as per sign convention described earlier. No sign should be attached to the unknown parameter during calculations. Its sign (- or +) will come on its own after calculations. MAGNIFICATION BY LENSES What is meant by magnification produced by lenses. The magnification is defined as The ratio of the size (height) of the image to the size (height) of the object is called magnification, or lateral magnification. Magnification is denoted by M. Magnification, M = Height of the image (hi) /Height of the object (ho )) = Distance of the image v/distance of the object from the lens u The magnitude of magnification of a lens gives information about the size of the image relative to that of the object. The sign of magnification of a lens gives information about the nature of the image produced by it. When the height of the image is positive, the magnification is positive, and when the height of image is negative, the magnification is negative. POWER OF A LENS The magnification of a lens is negative when it produces inverted (and real) image The magnification is positive when an erect (and also virtual) image is formed. What is meant by power of a lens Whenever a ray of light passes through a lens (except when it passes through the optical centre) it bends. The bending of rays towards the principal axis is called convergence, and bending away from the principal axis is called divergence. The degree of convergence or divergence of a lens is expressed in terms of its power. Power of a lens is defined as reciprocal of its focal length in metres. It is measured in dioptres denoted by the letter D. The dioptre unit is equal to m -1, i-e. 1 D = 1 m _1. The power of a lens is related to its focal length f by the relationship, Power of a lens = 1/ Focal length in m When the focal length of the lens is expressed in centimetres, then Power of a lens = 100/ Focal length in cm Sign of the power of lens. As per sign convention, the focal length of a convex lens is positive and that of a concave lens is negative. So, the power of a convex lens is positive, and that for a concave lens is negative. How is the power of a combination of lenses described Quite often we use a combination of lenses to minimise certain defects in the images produced by a single lens. The net power of a combination of lenses placed in contact is equal to the algebraic sum of the powers of all the lenses. For example, if lenses with individual powers P 1; P 2, P3,... are combined, then the net power (P) of the combination of these lenses is given P = P, + P 2 + P or 1/f = 1/f 1 +1/f 2 +1/f 3. Since the power of a lens is related to its focal length inversely, the above relationship can also be expressed as where f is the focal length of the combination of lenses and f1, f2, f 3, etc. are the focal lengths of the individual lens in the combination. Numerical Problems: 1. A concave lens of focal length 15 cm forms an image 10 cm from the lens. Find the distance of the object from the lens. [Ans. u = - 30 cm] 2. An object is placed 8 cm from a concave lens of focal length 24 cm. Where is the image formed and what is the magnification? [Ans. v = - 6 cm; M = 0.75; virtual, erect] 3. Find the position, size and nature of the image formed when an object 2 cm high is placed (a) 7.5 cm from a convex lens of focal length 5 cm [Ans. v = 15 cm; 4 cm; real, inverted] (b) 4 cm from a convex lens of focal length 12 cm [Ans. v = - 6 cm; 3 cm; virtual, erect] (c) 10 cm from a concave lens of focal length 10 cm.[ans. v= - 5 cm; 1 cm; virtual, erect] 4. A convex lens has a focal length of 10 cm. What is its power? [Ans. 10 D] 5. A person having a myopic eye uses a concave lens of focal length 50 cm. What is the power of the lens? ([Ans. 2 D] 6. The power of a lens is 5 dioptre. What is the focal length and type of the lens?[ans. 0.2 m; convex lens] 13 P a g e QUESTIONS FROM BOARD PAPERS Q.l. (a) State Snell's law of refraction of light. (b) A transparent medium A floats on another transparent medium B. When a ray of light travels obliquely from A into B, the refracted ray bends away from the normal. Which of the media A and B is optically denser and why?[ans. A is denser than B] Q.2. With the help of ray diagrams show the phenomenon of total internal reflection of light and the concept of critical angle for a transparent medium. Q.3. (?) What is meant by 'critical angle' for a ray of light going from one medium into another? (ii) What is the consequence of making angle of incidence of light at an interface, greater than the critical angle? (in) Why does a cut diamond shine more than a glass piece with diamond cut? Q.4. (a) Draw a ray diagram to show passage of two rays of light through a rectangular slab of glass, when the angle of incidence is zero in one case and a little less than 90 in the other case. (b) Prove that if a ray enters a rectangular glass slab obliquely and emerges from the opposite face, the emergent ray will be parallel to the incident ray. Q.5. A convex lens has a focal length of 25 cm. Calculate the distance of the object from the lens if the image is to be formed on the opposite side of the lens at a distance of 75 cm from the lens. What will be the nature of the image? [Ans. u = 37.5 cm, real, inverted and double the size of the object] Q.6. A 5 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 20 cm. The distance of the object from the lens is 30 cm. Find the (i) position, (ii) nature, and (iii) size of the image formed. Ans. v - 60 cm, real and inverted. 10 cm in height] Q.7. find the position, nature and size of the imago formed by a convex Ions of focal length 12 cm of an object 3 cm high placed at a distance 20 cm from it. Ans. v - 30 cm, real and Invertod. enlarged (4.5 cm in height)] Q.8. What will bo the focal length of a Ions whoso power is given as D?[Ans. 50 cm]