| a. |
A
student claims that the wave energy at the position of destructive interference
is zero because the wave energy is destroyed there. Comment on the claim
of the student. |
2
marks |
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The student's claim is incorrect. Energy cannot
be destroyed (nor can it be created). |
1 |
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Interference is effectively an re-distribution
of energy. |
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Positions of constructive interference receive
more energy, at the expense of the positions of destructive interference. |
0.5 |
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| b. |
Sketch
the experimental arrangement that could give rise to the formation of Newton’s
rings. Explain carefully the following observations:
i)
a dark fringe is formed at the center of the Newton’s rings when the reflected
light is viewed |
8
marks |
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2 |
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Interference occurs between light reflected at the upper
(ray 1) and lower (ray 2) surfaces of the air-gap. |
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There is no phase change for ray 1. But ray 2 undergoes
p phase change. |
1 |
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The overall optical path difference between the two rays
is |
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At the center of the Newton's ring, the thickness t
is zero. Thus, the optical path difference is |
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This corresponds to destructive interference. Hence, a
dark spot is seen. |
1 |
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ii)
a bright fringe is formed at the center when the transmitted light is viewed |
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Since the optical path for the two transmitted ray is zero,
constructive interference occurs. Thus, the centre of the rings for transmitted
light is bright. |
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iii)
the density of rings increases at higher orders. |
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1 |
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From equation (7), the thickness of the mth
dark fringe is given by |
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Let R be the radius of curvature of
the lens surface. The radius of the ring r is given by |
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Since t is small, t2
is negligible. Thus, the radius of the mth ring is given by |
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Thus, as m increases, the rate of increases
of r is not as rapid, i.e. The rings become denser for higher order. |
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| c. |
An
interferometer consists of a 45o-partial reflector that splits
a beam of monochromatic light into two. After reflections by two mirrors,
the two beams of light recombine to produce an interference pattern. Sketch
a diagram to show an interferometer. Describe and explain the result of
interference as one of the mirrors is gradually moved away from the partial
reflector. |
6
marks |
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2 |
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Light is split into two paths l1
and l2 by the partial reflector. After reflection by
mirrors M1 and M2 respectively, they
reach the same detector. |
1 |
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The overall optical path difference between
the two rays is |
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1 |
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If one of the mirrors moves, then the optical
path will change. |
1 |
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A bright fringe would be detected when |
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A dark fringe would be observed when |
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Thus, alternate bright and dark fringes would
be observed. |
1 |