Q. 1) What is the shape of the wave front in each of the following cases:
(a) Light diverging from a point source.
(b) Light emerging out of a convex lens when a point source is placed at its focus.
(c) The portion of the wavefront of light from a distant star intercepted by the Earth.
Ans:
(a) The wavefront of a light diverging from a point source is diverging spherical wavefront as shown in the given figure.
(b) When we put a point source at the focus of the convex lens, the rays of light emerging out of the convex lens become parallel. Thus, the wavefront of the light emerging out of the convex lens when a point source is placed at its centre is a plane wavefront as shown in the given figure.
(c) Since the star is at infinite distance from Earth, therefore, the portion of the wavefront of light from a distant star intercepted by Earth is a plane wavefront.
Q. 2) You have learnt in the text how Huygens’ principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.
Ans: Consider that a point object P is placed in front of a plane mirror M1M2 as shown in the given figure.
Draw a circle from the centre of the object P such that it touches the plane mirror at point O. As per Huygens principle, ST is the spherical wavefront of the incident light. In the absence of the plane mirror, a similar wavefront S′T′ would appear from behind point O whose distance is equal to the object distance from the centre of the mirror.
S′T′ can be treated as the virtually reflected image of ST. Therefore, we conclude that a point object placed in front of the plane mirror produces a virtual image whose distance from the mirror is equal to the distance of the object from the mirror.
Q. 3) Let us list some of the factors, which could possibly influence the speed of wave propagation:
(i) nature of the source
(ii) direction of propagation
(iii) motion of the source and/or observer
(iv) wavelength
(v) intensity of the wave
On which of these factors, if any, does
(a) the speed of light in vacuum,
(b) the speed of light in a medium (say, glass or water), depend?
Ans:
(a) The speed of light in vacuum i.e., 3 × 108 ms−1 (approximately) is an absolute constant. It is not affected by any of the factors listed above.
(b) Among the tabulated factors, the speed of light in a medium depends only on the wavelength of light in that medium.
Q. 4) For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest; observer moving, and (ii) source moving; observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?
Ans: Sound waves cannot propagate in vacuum. Sound waves require a material medium for their propagation. In case of the given two situations, the motion of the observer w.r.t. the medium is different. That is why, the Doppler’s formula for given two situations cannot be scientifically identical to each other in case of sound waves.
However, light waves can travel in vacuum as well. The velocity of light waves is constant in the vacuum. Since the velocity of light in the vacuum is independent of the speed of observer and speed of the source, the Doppler’s formulae for light waves in vacuum are exactly similar in case of the given two situations.
However, when light propagates in a medium, the given two situations are not exactly identical. This is due to the fact that the speed of light in a medium depends on the optical density of the medium.
Q. 5) Answer the following questions:
(a) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band?
(b) In what way is diffraction from each slit related to the interference pattern in a double-slit experiment?
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the shadow of the obstacle. Explain why?
(d) Two students are separated by a 7 m partition wall in a room 10 m high. If both light and sound waves can bend around obstacles, how is it that the students are unable to see each other even though they can converse easily.
(e) Ray optics is based on the assumption that light travels in a straight line. Diffraction effects disprove this assumption. Yet the ray optics assumption is so commonly used. What is the justification?
Ans:
(a) In a single slit diffraction experiment, if the width of the slit is doubled, the size of the central diffraction band reduces to half and its intensity becomes four times the original value.
(b) If the width of each slit is of the order of the wavelength of the light used, then the diffraction of light from each slit will modulate the interference pattern in the double slit experiment.
(c) When a tiny circular obstacle is placed in the path of light from a distant source, the light waves diffract from the edges of the circular obstacle to produce the constructive interference at the centre of the shadow of the obstacle which is responsible for the bright spot.
(d) The wavelength of light is very small as compared to the size of the wall, so bending of light waves by a large angle is not possible. Hence, the students are unable to see each other. The wavelength of sound waves is comparable to the size of the wall, hence sound bends easily and they can converse.
(e) Since the wavelength of light used is very small as compared to the aperture of optical instruments, diffraction effects are not significant. Therefore, ray optics approximation is valid.
Q. 6) Answer the following questions:
(a) When a low flying aircraft passes overhead, we sometimes notice a slight shaking of the picture on our TV screen. Suggest a possible explanation.
(b) The principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification?
Ans:
(a) When a low flying aircraft passes overhead the reflected radio waves may interfere with the normal TV signal coming from the antenna and result in shaking of the picture.
(b) Since the principle of superposition follows from the linear character of the differential equation of wave motion, it is basic to understanding diffraction and interference patterns.
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