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Review - Waves and Light

Modified True/FalseIndicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the sentence or statement true.

____ 1. A wave ray indicates the direction of energy propagation for a wave. _________________________

____ 2. As water waves enter a deeper medium, they speed up and their wavelength shortens. _________________________

____ 3. The angle of incidence equals the angle of refraction. _________________________

____ 4. The angle of incidence can be measured between the incident wave front and the boundary. _________________________

____ 5. Total internal reflection occurs when the incident angle is equal to the critical angle. _________________________

____ 6. As the size of an opening decreases, the amount of diffraction increases. _________________________

____ 7. Higher frequencies of sound bend through a doorway more easily. _________________________

____ 8. Michelson's interferometer was used to disprove the existence of an “ether” filling all of space. _________________________

____ 9. Waves of longer wavelength experience more diffraction than those of shorter wavelength. _________________________

____ 10. For diffraction to be observable, the slit width w must be greater than or equal to the wavelength . _________________________

____ 11. Destructive interference occurs when the resultant waveform has a smaller amplitude than each individual wave. _________________________

____ 12. Nodal lines occur at points of continual constructive interference. _________________________

____ 13. Decreasing the wavelength of the sources causes nodal lines in a two-point source interference pattern to move closer together. _________________________

____ 14. The difference in path lengths from a point on a given nodal line to the two sources in a two-point source interference pattern is directly proportional to the wavelength of the sources. _________________________


____ 15. It is generally accepted that light exhibits only wave properties. ______________________________

____ 16. Christiaan Huygens was a strong supporter of the particle theory of light. _________________________

____ 17. The wave theory of light was superior in explaining the phenomenon of diffraction. _________________________

____ 18. Young’s double-slit experiment was designed to illustrate that light exhibits interference patterns. _________________________

____ 19. In light, longer wavelengths refract less than shorter wavelengths. _________________________

____ 20. The wave theory of light must be used to properly explain dispersion. _________________________

CompletionComplete each sentence or statement.

21. When creating water waves in a ripple tank, the ____________________ appear as bright areas on the screen below.

22. When the wavelength of a wave ____________________, the amount of noticeable diffraction increases.

23. When generating a two-point source interference pattern in a ripple tank, increasing the frequency of the sources causes the wavelength to ____________________.

24. In Young’s double-slit experiment, a(n) ____________________ is produced at the centre of the pattern.

25. The observation that nodal lines are more spaced out for red light than for blue light indicates that red light has a(n) ____________________ wavelength than blue light.

26. The bending of a wave due to changing speed is called ____________________.

27. The bending of a wave around corners or through openings is called ____________________.

28. Light that is composed of a single colour, or wavelength, is called ____________________.


29. ____________________ defines the mathematical relationship between the angles of incidence and refraction.

30. ____________________ interference occurs when the resultant waveform has a larger amplitude than each individual wave.

31. Nodal lines in a two-point source interference pattern have a ____________________ shape.

32. The “corpuscular” theory of light was most strongly supported by ____________________.

33. The sharpness of shadows supports the property of light referred to as ______________________________.

34. A student observes white light entering a triangular prism and emerging in its spectral colours on the other side. This phenomenon is called ____________________.

35. Red light bends least. According to Snell’s law, the wavelength of red light is ____________________ that of blue light.

Short Answer1. Young’s experiment was instrumental in supporting Huygens’ wave theory of light.

Explain which two conditions Young satisfied in his experiment that were not adequately done before. Describe how he achieved these two conditions.

2. The diagram shown below illustrates the possible paths followed by a light ray as it enters a lens (n = 1.56) covered with a thin coating (n = 1.25). If the thin coating has a thickness of, what type of interference occurs with rays 3 and 4.

Explain your answer.

3. Two water taps, closely separated, randomly drip into a sink that is half filled with water. Each water droplet acts as a source for a circular wavefront. Even though there are two


sources continually creating water waves, no interference pattern is noticed. What two conditions necessary to produce visible interference have not been met?

4. An astute student performs Young’s double slit experiment in water (nwater = 1.33) and observes an interference pattern. The student then performs an identical experiment in flint glass (nglass = 1.66) using the same equipment and distances. What changes would be noticed in the interference pattern?

Problems1. A two-point source interference pattern is generated in a swimming pool. A piece of styrofoam, located on the second nodal line, is 12.0 m from one source and 20.0 m from the other source. One wave crest takes 2.0 s to travel the 35.0 m width of the pool. Find the speed, wavelength, and frequency of the waves. 2. Blue light with a wavelength of 475 nm is passed through a double slit with a separation of 22.6 mm. What is the maximum number of nodal lines visible in the entire pattern?

3. Light travels in water at three-quarters the speed it attains in air. If the angle of incidence in air were 10.0°, what would be the angle in water, according to particle theorist.

4. A laser emitting 632.8 nm illuminates a double slit. A screen is positioned 2.00 m from the slits. Interference fringes are observed with a separation of 1.0 cm.

a) Determine the separation of the slits.

b) Determine the angle of the first-order dark fringes.

5. In a double-slit experiment, blue light of wavelength 4.60 x 10² nm gives a second order maximum at a certain location P on the screen. What wavelength of visible light have a minimum at P?

6. In young’s experiment while using a source of light of wavelength 5000 x10−10 m, the fringe width obtained is 0.6 cm. If the distance between the screen and slit is reduced to half, what should be the wavelength of the source to get fringes 0.4 cm wide?


7. A water wave in a ripple tank travels from a shallow to a deep region. The wavelength and speed in the shallow region are 2.5 cm and 5.0 cm/s, respectively. If the wavelength in the deep region is 6.0 cm, find

(a) The relative index of refraction from shallow to deep water

(b) The speed of the wave in the deep water.

8. A water wave travels from region 1, where the wavelength is 7.5 cm and the angle of incidence is 45o, into region 2 where the angle of refraction is 25o. What is the wavelength in region 2?

9. A student performs Young's double-slit experiment using a slit separation of 21.6 m. A screen is placed 2.50 m from the centre of the sources such that a point on the fifth nodal line is 37.5 cm from the centre of the interference pattern. Find the wavelength of the light used and identify its colour.


Solutions :

Modified True/FalseIndicate whether the sentence or statement is true or false. If false, change the identified word or phrase to make the sentence or statement true.

__T_ 1. A wave ray indicates the direction of energy propagation for a wave. _________________________

___F_ 2. As water waves enter a deeper medium, they speed up and their wavelength shortens. ___LENGTHENS/INCREASES___

__F__ 3. The angle of incidence equals the angle of refraction. ____REFLECTION _____________________

__T__ 4. The angle of incidence can be measured between the incident wave front and the boundary. _________________________

__F__ 5. Total internal reflection occurs when the incident angle is equal to the critical angle. _________IS GREATER THAN________________

___T_ 6. As the size of an opening decreases, the amount of diffraction increases. _________________________

___F_ 7. Higher frequencies of sound bend through a doorway more easily. ____LOWER_____________________

_T___ 8. Michelson's interferometer was used to disprove the existence of an “ether” filling all of space. _________________________

__T__ 9. Waves of longer wavelength experience more diffraction than those of shorter wavelength. _________________________

__F__10. For diffraction to be observable, the slit width w must be greater than or equal to the wavelength. ______LESS THAN OR EQUAL TO___________________

__T__11. Destructive interference occurs when the resultant waveform has a smaller amplitude than each individual wave. _________________________

__F__12. Nodal lines occur at points of continual constructive interference. ______DESTRUCTIVE INTERFERENCE___________________

__T__13. Decreasing the wavelength of the sources causes nodal lines in a two-point source interference pattern to move closer together. _________________________


__T__14. The difference in path lengths from a point on a given nodal line to the two sources in a two-point source interference pattern is directly proportional to the wavelength of the sources. _________________________

__F__15. It is generally accepted that light exhibits only wave properties. BOTH WAVE AND PARTICLE PROPERTIES ______________________

_F___16. Christiaan Huygens was a strong supporter of the particle theory of light. WAVE THEORY_______________________

__T__17. The wave theory of light was superior in explaining the phenomenon of diffraction. _________________________

_F___18. Young’s double-slit experiment was designed to illustrate that light exhibits interference patterns. DIFFRACTION_________________________

__T__19. In light, longer wavelengths refract less than shorter wavelengths. _________________________

__T__20. The wave theory of light must be used to properly explain dispersion. _________________________

CompletionComplete each sentence or statement.

21. When creating water waves in a ripple tank, the ____CRESTS________________ appear as bright areas on the screen below.

22. When the wavelength of a wave _____INCREASES_______, the amount of noticeable diffraction increases.

23. When generating a two-point source interference pattern in a ripple tank, increasing the frequency of the sources causes the wavelength to _DECREASE________________.

24. In Young’s double-slit experiment, a(n) _ANTINODAL LINE/MAXIMUM_ is produced at the centre of the pattern.

25. The observation that nodal lines are more spaced out for red light than for blue light indicates that red light has a(n) _____LONGER_______________ wavelength than blue light.

26. The bending of a wave due to changing speed is called ___REFRACTION_________________.

27. The bending of a wave around corners or through openings is called __DIFFRACTION__________________.


28. Light that is composed of a single colour, or wavelength, is called _____MONOCHROMATIC_______________.

29. _____SNELL’S LAW_______________ defines the mathematical relationship between the angles of incidence and refraction.

30. ____CONSTRUCTIVE________________ interference occurs when the resultant waveform has a larger amplitude than each individual wave.

31. Nodal lines in a two-point source interference pattern have a ___HYPERBOLIC_____ shape.

32. The “corpuscular” theory of light was most strongly supported by _ISSAC NEWTON_______.

33. The sharpness of shadows supports the property of light referred to as RECTILINEAR PROPOGATION.

34. A student observes white light entering a triangular prism and emerging in its spectral colours on the other side. This phenomenon is called ____DISPERSION________________.

35. Red light bends least. According to Snell’s law, the wavelength of red light is _LONGER THAN __ that of blue light.

SHORT ANSWERS:

1. - In order to see a stationary interference pattern, the phase of the two sources must be constant, and the two narrow sources close together.

- By using a single bulb and two very narrow pinholes placed close together, Young was able to satisfy both of these conditions, allowing a stationary diffraction pattern to be observed

2. Constructive interference occurs between the rays. Since ray 3 passes straight through, its phase is unchanged. Ray 4 is reflected from a more dense surface, so its phase is inverted when it reflects from the lens surface, but not inverted when it reflects from the air. Since ray 4 has travelled a total of half a wavelength farther, the two rays are in opposite phase; however, the extra inversion of wave 4 brings them back into phase. Hence, constructive interference occurs.

3. The sources are not in phase since they are randomly dripping. The sources are not likely producing waves of the same frequency and wavelength.


4. Since the speed of light is slower in flint glass than in water, the wavelength of the source would decrease. Shorter wavelengths diffract less and, thus, the diffraction pattern seen would be less spread out (i.e., the average spacing between bright fringes would decrease).

PROBLEMS:


Q 7.

(a)

The relative index of refraction from shallow to deep water is 0.42.


(b)

The speed of the wave in the deep water is 12 cm/s.

Q 8.

The wavelength in region 2 is 4.5 cm.


Q9.

The colour used was red with a wavelength of 7.20 x 10-7 m.

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