Point to be remembered: sign convention for Spherical mirror Object height, h = always positive Always +ve for virtual image Image height h = Always ve for real image. Object distance from pole (u) = always negative always positive for virtual image Image distance from pole (v)= always negative for real image Positive for convex mirror Focal length (f) = Negative for concave mirror REFRACTION OF LIGHT: The phenomenon of bending of light as it passes from one medium to another medium is called refraction of light. The refraction is caused due to change in velocity of light as it passes from one medium to another medium. Rarer medium Denser medium Angle of refraction Rarer medium Denser medium r Refracted ray Incident ray i Angle of incidence When ray of light travels from a rarer medium to a denser medium, it bends towards the normal When ray of light travels from a denser medium to a rarer medium, it bends away from the normal. Note: Speed of light decreases as the beam of light travel from rarer medium to the denser medium. Some Commonly observed phenomenon due to Refraction
1. The stone at the bottom of water tub appear to be raised. 2. A fish kept in aquarium appear to be bigger than its actual size. 3. A pencil partially immersed in water appears to be displaced at the interface of air and water. Refraction of light through a Rectangular Glass Slab When an incident ray of light AO passes from a rarer medium (air) to a denser medium (glass) at point O on interface PQ, it will bends towards the normal. At point B, on interface SR the light ray entered from denser medium (glass) to rarer medium (air) here the light ray will bend away from normal OB is a refracted ray BC is an emergent ray. If the incident ray is extended to D, we will observe that emergent ray BC is parallel to incident ray. The ray will slightly displace laterally after refraction. Note: When a ray of light is incident normally to the interface of two media it will go straight, without any deviation. The perpendicular distance between the direction of the incident ray and emergent ray is called lateral displacement or lateral shift. Factors on which lateral shift depends on : 1. Angle of incidence 2. Thickness of the glass slab 3. Refractive index of the glass slab. Laws of Refraction: 1. The incident ray, the refracted ray and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane. 2. The ratio of sine of angle of incidence to the sine of angle of refraction is a constant, for the light of given colour and for the pair of given media. This law is also known as Snell`s law of refraction. If i is the angle of incidence and r is the angle of refraction, then The constant is called refractive index of the second medium with respect to the first. Refractive index : The absolute refractive index of a medium is the ratio of the speed light in air or vacuum to the speed of light in medium.
Refractive index (n) = ie, n = Note: C Speed of light in vacuum = 3 10 8 m/s RELATIVE REFRACTIVE INDEX: The relative refractive index of a medium 2 with respect to a medium 1 is the ratio of the speed of light in medium 1 to the speed of light in medium 2. Note: Light will travel faster in the medium having lower value of refractive index Refractive index of water (n w ) = 1.33 Refractive index of glass (n g ) = 1.52 Refractive index has no unit. The absolute refractive index of a medium is simply called refractive index Spherical Lens: A transparent material bound by two surface, of which one or both surfaces are spherical, forms a lens. Types of Spherical lenses: 1. Convex lens : A lens may have two spherical surfaces, bulging outwards, is called double convex lens (or simply convex lens. It is thicker in the middle and thinner at the edges. It is also known as converging lens because it converges the light. 2. concave lens : A lens bounded by two spherical surfaces, curved inwards is known as double concave lens (or simply concave lens).it is thinner in the middle and thicker at the edges. It is also known as diverging lens because it diverges the light. Terms related to spherical lens: 1) Convex lens : Principal Axis R C F 1 O F 2 C 2 f 1 or (2F 1 ) Optical centre(o) Or (2F 2)
2) Concave lens: 1. Centre of curvature - A lens, either a convex lens or a concave lens has two spherical surfaces. Each of these surfaces form a part of sphere. The centre of these two spheres are called centre of curvature represented by C 1 and C 2. 2. Principal axis - Imaginary straight line passing through the two centres of curvature 3. Optical Centre - The central point of lens is its optical centre (O). A ray of light, when passes through 'O' it remains undeviated i.e. it goes straight. 4. Aperture - The effective diameter of the circular outline of a spherical lens. 5. Focal length - The distance between optical centre and principal focus is called focal length of a lens. Focal length of a lens is half of the radius of curvature. Tips for drawing Ray diagram a) After refraction, a ray parallel to principal axis will pass through F. F 1 O F 2 O F2 F 1 Principal Axis (Converge) (Diverge) b) A ray passes through F, after refraction will emerge parallel to principal axis Convex lens Concave lens
Image formation by a convex lens for various position of object: Case 1: Object at infinity Position of the image: At Focus F2 Nature of the image : Real and inverted : Highly diminished or Point sized. Case 2: Object beyond 2F1
Position of the image: Between F2 and 2F2 Nature of the image : Real and inverted : Diminished. Case 3: Object at 2F1 Position of the image: At 2F2 Nature of the image : Real and inverted : Same size. Case 4: Object between F1 and 2F1 Position of the image: Beyond 2F2 Nature of the image : Real and inverted
: Enlarged. Case 5: Object at F1 Position of the image: At infinity. Nature of the image : Real and inverted. : Highly enlarged. Case 6: Object between F1 and optical centre O Position of the image: On the same side of the lens as the object. Nature of the image : Virtual and erect. : Enlarged.
Image formation by a concave lens for various position of object: Case 1: Object at infinity Position of the image: At Focus F1 Nature of the image : Virtual and erect. : Highly diminished or Point sized. Case 2: Object between infinity and optical centre O Position of the image: Between F1 and optical centre O Nature of the image : Virtual and erect. : Diminished Sign Convention for Refraction by spherical lens: Similar to that of spherical mirror, only the difference is that all the measurement are made from optical centre 'O' LENS FORMULA : =
Where, f = f focal length of the lens v Image distance u Object distance R Radius of curvature MAGNIFICATION: It is expressed as the ratio of the height of the image to height of the object. m= ( ) ( ) 1 It is also related to u and v m = 2 Comparing eqn 1 and 2 we can write, Note: m = = If magnitude of m > 1 Image is magnified m = 1 Image is of same size m < 1 Image is diminished. Point to be remembered: sign convention for Spherical Lens: Object height, h = always positive Always +ve for virtual image Image height h = Always ve for real image. Object distance from optical centre (u) = always negative always negative for virtual image Image distance from optical centre (v)= always positive for real image
Power of Lens: The degree of convergence or divergence of light ray achieved by a lens is known as power of a lens. It is defined as the reciprocal of its focal length (inmetre)represented by P P = ( ) Or, P = ( ) Note: SI unit of power of a lens is "dioptre" denoted by 'D' Definition of 1dioptre (1D) : 1 dioptre is the power of a lens whose focal length is 1 metre. 1D = 1m -1 Power convex lens or converging lens is always positive f is +ve Power of concave lens or diverging lens is always negative f is ve If any optical instrument have many lens, then net power will be P = P 1 + P 2 + P 3...