Optics 6 Question 55
57. A narrow monochromatic beam of light of intensity $I$ is incident on a glass plate as shown in figure. Another identical glass plate is kept close to the first one-and parallel to it. Each glass plate reflects 25 per cent of the light incident on it and transmits the remaining. Find the ratio of the minimum and maximum intensities in the interference pattern formed by the two beams obtained after one reflection at each plate.
(1990, 7M)
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Answer:
Correct Answer: 57. $\frac{1}{49}$
Solution:
- Each plate reflects $25 %$ and transmits $75 %$.
Incident beam has an intensity $I$. This beam undergoes multiple reflections and refractions. The corresponding intensity after each reflection and refraction (transmission) are shown in figure.
Interference pattern is to take place between rays 1 and 2 .
$$ \begin{array}{rlrl} & I _1=\frac{I}{4} \text { and } I _2=9 I / 64 \\ \therefore \quad & \frac{I _{\min }}{I _{\max }} & =\frac{\sqrt{I _1}-\sqrt{I _2}}{\sqrt{I _1}+\sqrt{I _2}}=\frac{1}{49} \end{array} $$
