Answers to SNC 2DI Review for Unit Test #3: Geometric Optics

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1 Answers to SNC 2DI Review for Unit Test #3: Geometric Optics 1. Know the meanings of the following terms and be able to apply them for multiple choice questions: physics non-luminous regular reflection diverging lens optics incandescent diffuse reflection optical centre light luminescent concave mirror real focus photon transparent convex mirror virtual focus wavelength translucent refraction myopia amplitude opaque refractive index far-sighted frequency umbra total internal reflection hyperopia Hertz penumbra critical angle near-sighted luminous optical device converging lens 2. Be able to convert numbers between scientific notation and expanded form = x x 10 5 = = 5.87 x x 10 4 = = 3.05 x x 10 6 = = 1.4 x x 10 3 = Use the conversion factor method to convert between the following units. You must know the conversion factors and please show all work. a) 740 nm to meters = m or 7.4 x 10 7 m b) 4.50 m to nm = nm or 4.5 x 10 9 nm c) 120 km/h to m/s = 33.3 m/s d) 62 m/s to km/h = km/h 4. What is the speed of light in a vacuum? 3.00 x 10 8 m/s Convert this to km/h x 10 9 km/h 5. We have studied four laws related to light. State each law and describe one application or use of each law: a) The Law of Conservation of Energy: energy can neither be created nor destroyed but it can be converted between different forms. For example, we can convert many different types of energy to light: mechanical energy to light eg. mechanoluminescence (crushing wintogreen candies) nuclear energy to light when small atoms smash together in the sun chemical energy when chemical reactions produce light b) The Law of Reflection: the angle of incidence is equal to the angle of reflection when measured from the normal. This law allows us to predict the location of images in plane and curved mirrors. c) The three Laws of Refraction: when light travels from a less dense to a more dense substance at an angle, it slows down and bends toward the normal. This can be used to explain why light bends when it moves from the air into a prism as shown in the picture to the right. when light travels from a more dense to a less dense substance at an angle, it speeds up and bends away from the normal. This can be used to explain why the light leaving the prism and re-entering the air speeds up and emerges parallel to the first incident ray. It is also used to explain why light bends when it leaves the water and enters the air so objects appear to be closer to the surface of the water than they really are. when light travels from a less dense to a more dense substance and hits the surface exactly along the normal, it slows down but does not bend. This is useful to explain why light that shines down straight into the water does not bend.

2 d) Snell s Law: n 1 sine θ 1 = n 2 sine θ 2 This law can be used to predict the angle of refraction if the indexes of refraction and incident angles are known. It can also be used to determine the index of refraction of an unknown substance (eg. fake diamonds) to identify them. 6. Be able to calculate frequency of a wave or repeating event for a multiple choice question. a) Natalia Kanounnikova holds the record for the world s fastest spin on ice skates. If she made 308 complete revolutions in one minute, what was her frequency in Hertz? frequency = cycles/second = 308 revolutions/ 60 s = 5.13 Hz (cycles per second) b) a NASCAR driver completes 200 laps in 2 hours and 32 minutes. What is this frequency in Hertz? frequency = cycles/second = 200 laps/ 9120 s = Hz (laps per second) 7. Be able to label the trough, crest, rest position, wavelength and amplitude on a diagram of a wave. a) What is the importance (significance) of the wavelength of light? Wavelength determines the amount of energy that the electromagnetic radiation has. In the case of visible light, it is the wavelength that determines the colour of the light. b) What is the importance (significance) of the amplitude of light? The amplitude of a wave determines its intensity. In the case of light, amplitude determines the intensity or brightness of the light. c) What is the importance (significance) of the frequency of light? The frequency of light is another indication of its wavelength or energy. The higher the frequency, the shorter the wavelength and the higher the energy. 8. For the seven different types of electromagnetic radiation, know their: a) relative wavelengths (from longest to shortest): radio > microwave > infra-red > visible light > ultra-violet > X-rays > gamma rays b) relative energy (from lowest to highest energy) radio > microwave > infra-red > visible light > ultra-violet > X-rays > gamma rays c) speed in a vacuum is always 3.00 x 108 m/s for all types of electromagnetic radiation (the speed of light depends only on the medium it is travelling through) d) two applications (uses) of each: radio waves are used for radios and cell phone communication microwaves are used for microwave ovens and telecommunication by satellite infra-red is another name for heat, it is used for warming lights and burglar alarms visible light is used for human vision, rainbows, lighting systems etc ultra-violet is used for security devices on money, by flowers to attract insects and in our skin to make vitamin D (it also causes sun burn) X-rays are used for medical imaging and to inspect the containers of trucks gamma rays are used to sterilize medical equipment and for radiation treatments for cancer 9. Understand and be able to apply Additive Colour Theory: Additive Colour Theory states that white light is made up of all of the colours of light added together. By adding specific colours of light together, we can create all of the colours of light. a) What are the primary and secondary additive colours? the primary additive colours are red, green and blue the secondary additive colours are magenta, cyan and yellow rest position b) Explain how Additive Colour Theory is used in LCD televisions. An LCD television screen contains hundreds (thousands?) of liquid crystals that can produce only red, green or blue light. The crystals are lit up in different combinations and intensities so that their light is added together to produce all of the shades of colour.

3 10. Understand and be able to apply Subtractive Colour Theory: Subtractive Colour Theory states that black light is the absence of all light. If white light shines on an object, pigments in that object absorb some colours of light, and reflect whatever colours they don t absorb. It is the reflected colours that determine what colours of light reach our eyes and these are the colours we see. a) What are the primary and secondary additive colours? the primary subtractive colours are magenta, cyan and yellow the secondary subtractive colours are red, green and blue b) Give two applications or situations where Subtractive Colour Theory is used. subtractive colour theory is used in making pigments and dyes to cause objects to appear certain colours. For example, pigments in a red rose absorb green and blue light. By subtracting these colours from white light, the rose reflects only red light and this is what we see. Similarly, colour printers contain only cyan, magenta and yellow colour jets. These primary subtractive colours can be mixed to produce all of the colours we want when we are printing. 11. Are black and white colours? Explain. black and white are not actually colours. White is all of the colours added together, while black is the absence of any colour at all. 12. What are two properties of light? What determines the speed that light travels? light travels in straight lines light travels at a speed of 3.00 x 10 8 m/s in a vacuum the speed of light is determined by the density of the medium (substance) it is travelling through 13. What three ways can light be produced by luminous objects? Give two examples of each. light can be produced by nuclear reactions. Nuclear reactions can occur two ways. If two small nuclei smash together, they can fuse to form one large atom and release energy as light. This is what takes place in the sun and stars. A large atom can split apart into two or more smaller atoms and release energy as light. This is what occurs in nuclear reactors and bombs. light can be produced by incandescence. This is when objects are heated to very high temperatures and then give off energy as light. This takes place in incandescent lightbulbs and the elements of electric stoves and toasters. light can be produced by luminescence. This is when the electrons in atoms are excited by the addition of energy. The electrons jump away from the nucleus to higher energy levels. Eventually the electrons drop back closer to the nucleus and release their energy as light. Luminescence is classified by the source of the energy used to excite the electrons. For example, magnesium burns and gives off light by chemiluminescence. Phosphorescent objects absorb light from radiant energy and then release it as visible light. 14. What three things can happen to light when it hits the surface of an object? When light hits a surface, it can be reflected, transmitted or absorbed. If it is transmitted, it may be refracted (bent) depending on the angle of incidence and refractive indexes. 15. Understand and be able to explain what happens in an atom when light is produced by luminescence. see the third point in question 13 a) for any four different types of luminescence, state the type of energy that is converted to light chemiluminescence is the conversion of chemical energy to light energy during chemical reactions, such as burning wood or magnesium bioluminescence is the conversion of chemical energy to light energy by living things such as fireflies and deep sea fish photoluminescence is the conversion of the energy from electromagnetic radiation to visible light, for example, phosphorescent and fluorescent substances absorbing ultra-violet radiation and releasing visible light mechanoluminescence is the conversion of mechanical energy to light, for example the energy from friction when we crushed a wintogreen mint electroluminescence is the conversion of electrical energy to light, such as occurs in lightning or plasma balls b) give an example for each of the types of luminescence you described above (see above)

4 normal 16. Describe how three different types of light bulbs produce light. Compare the efficiency of these three different types of light bulbs. incandescent light bulbs create light by first becoming very hot. Electricity passes through a tungsten filament, which becomes so hot that it gives off light. Because electricity if first converted to heat, and then light, these are your least efficient light bulbs fluorescent light bulbs create light when electricity excites the electrons in atoms of mercury within the bulb. When the electrons drop back to lower energy levels closer to the nucleus, they release ultra violet light. The UV light strikes a phosphor lining inside the bulb which then gives off white light. Fluorescent bulbs are more efficient than incandescent bulbs, but they still involve two energy conversions, so they are not as efficient as LEDs LEDs give light by converting electricity directly to light through a silicon semi-conductor. Because light is produced in only one step, these are the most efficient light bulbs. 17. We have used three different models of light to explain different aspects of light s behaviour. a) What model did we use to explain colour? Use this model to explain how the colours of light differ. We used the wave model of light to explain colour. In this model, the wavelength of light determines how much energy the light carries and this determines its colour. b) What model did we use to explain reflection? Use this model to explain the Law of Reflection. We used the ray model of light to explain reflection. The ray model shows light travelling in straight lines until it hits something. If it hits a smooth, regular surface, all of the light rays are reflected off the surface at the same angle they hit is (measured from the normal) and the reflected rays can be used to create an image. c) What model did we use to explain refraction? Use this model to explain the Law of Refraction that states that light slows down and bends toward the normal when it enters a more dense medium. We used the particle model of light to explain refraction. In this model, light is made of up streams of particles called photons. When photons hit a transparent or translucent surface at an angle, they enter the substance but are slowed down. When they strike the surface at an angle, the first photons to hit slow down first but the rest keep going at the faster speed. The slower photons bend toward the normal. Then the next streams of photons hit and are slowed down and bend, then the next and so on until the beam of light has all entered and bent toward the normal. 18. What is a shadow? Explain how the following factors affect the characteristics of a shadow: a shadow is a dark area that receives little or no light because the light has been blocked by a translucent or opaque object. a) the size of light source: the larger the light source, the larger and more blurry the shadow because it has a larger penumbra b) the size of the object: the larger the object, the larger the shadow because the object can block more light c) the transparency of object: the more transparent an object, the more light it allows to pass through and the lighter the shadow. Transparent objects can not create shadows, translucent objects create pale shadows (penumbras) and opaque objects create very dark shadows (umbras) d) the location of object: the closer the object is to the light source, the larger the shadow. 19. On the diagram to the right: a) label the normal, incident ray, refracted ray, reflected ray, angle of reflection and angle of refraction b) measure the angles of incidence, reflection and refraction c) does the second medium have a higher or lower refractive index than the first medium? the second medium must have a higher refractive index because the refracted ray bent toward the normal so the light had to slow down d) how does the speed of the reflected ray compare with the incident ray? incident ray Ө i Ө r Ө R reflected ray the speed of the reflected ray is equal to the speed of the incident ray because the reflected light is travelling in the same medium and it is the medium that determines the speed of light e) how does the speed of the refracted ray compare with the incident ray? the speed of the refracted ray is slower than the speed of the incident ray because the light refracted toward the normal f) What two laws does this diagram portray? refracted ray the Law of Reflection (the angle of incidence is equal to the angle of reflection when measured from the normal) and the Law of Refraction that states that light will slow down and bend toward the normal when it enters a more optically dense substance

5 20. Calculate the magnification of the image in the diagram to the right. magnification = hi / ho 21. Explain why objects under water appear to be closer to the surface than they really are. Draw a diagram to illustrate your answer. when light leaves an object from underwater, it enters the air and travels toward our eye. When the light leaves the water, it speeds up and bends away from the normal. Our eye can not see the light bending, so we extend the refracted ray straight back into the water, and this is where we think the light comes from. Because of the angle of refraction, the object appears to be closer to the surface of the water, as shown in the diagram. 22. Draw a diagram and explain in words how total internal reflection takes place. What two conditions must be met in order for total internal reflection to occur? total internal reflection takes place when light travels from a more dense substance to a less dense substance. At the critical angle, the light is refracted back along the surface of the water. If the incident angle is greater than the critical angle, the light is refracted so much that it is actually reflected back into the first medium. This is total internal reflection. in order to have total internal reflection, the light must be travelling from a more dense to a less dense substance, and it must strike the surface at an incident angle that is greater than the critical angle. 23. Explain how optical fibres allow light to go around corners. What are three advantages of optical fibres over copper wire for carrying information? read the note on optical fibres on the back of the note on Total Internal Reflection 24. Light travels from water into corn oil, hitting the surface at an angle of 42º. What is the angle of refraction? Givens: water corn oil n 1 = n 2 = 1.47 Ө 1 = 42º Ө 2 =? n 1 sine θ 1 = n 2 sine θ 2 (1.333) (sin 42º) = (1.47) (sin Ө 2 ) (1.333) (0.669) = (1.47) (sin Ө 2 ) (1.47) (1.47) = sin Ө 2 Substance Refractive Index Air Water (liquid) Alcohol Corn oil 1.47 Pyrex glass 1.47 Plexiglass 1.49 Crown glass Flint glass 1.61 Cubic Zirconium 2.16 Diamond sin Ө 2 = 37º therefore, the angle of refraction is 37º in the corn oil

6 25. Companies have recently learned how to make Moissanite, a mineral that is almost indistinguishable from diamond. Moissanite is made of silicon carbide while diamond is pure carbon. If light travels from air into Moissanite at an angle of 45.0º, it is refracted at an angle of 15.4º. Calculate the refractive index of Moissanite. Givens: air Moissanite n 1 = n 2 =? Ө 1 = 45.0º Ө 2 = 15.4º n 1 sine θ 1 = n 2 sine θ 2 (1.0003) (sin 45.0º) = (n 2 ) (sin 15.4º ) (1.0003) (0.707) = (n 2 ) (0.266 ) (0.266) (0.266) 2.66 = n 2 therefore, the refractive index of Moissanite is What is the speed of light in Moissanite? n = c or v = c v n v = 3.0 x 10 8 m/s 2.66 v = 1.13 x 10 8 m/s 27. If light travels at a speed of x 10 8 m/s in an unknown substance, calculate the refractive index of this substance. What is the likely identity of this substance? n = c n n = 3.0 x 10 8 m/s x 10 8 m/s = 1.61 so this material is probably flint glass 28. Compare near-sightedness and far-sightedness: Medical name for this condition What is wrong in the eye? (2 possibilities) near-sightedness myopia The lens in the eye focuses the image in front of the retina. This can happen because the person s eyeball is too long, or because the lens has too much curvature and converges the light too much. far-sightedness hyperopia The lens in the eye focuses the image behind the retina. This can happen because the person s eyeball is too short, or because the lens does not have enough curvature (is too flat) and does not converge the light enough. What type of lens is used to correct it and why? A diverging lens is used to treat myopia. It spreads the light entering the eye out, so that when the eye of the lens causes it to converge, it will focus on the retina. A converging lens is used to treat hyperopia. It converges the light entering the eye just slightly, so that when the eye of the lens converges it again, it will focus on the retina.