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Q.

A ray of light is incident on the surface of a glass plate of thickness t. If the angle incidence $θ$ is Small, the emerging ray would be displaced sideways by an amount (take refractive index of glass as n

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a

$t θ n / (n + 1)$

b

$t θ (n - 1) / n$

c

$t θ n / (n - 1)$

d

$t θ / (n + 1) / n$

answer is B.

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Detailed Solution

$If θ is small then \sin θ ≅ θ and \cos θ ≅ 1,$
$\begin{array}{l} \Rightarrow μ = \frac{\sin i}{\sin r} = \frac{i}{r} \Rightarrow r = \frac{i}{μ} \\ x = \frac{tsin (i - r)}{\cos r} = \frac{t (i - r)}{1} = t (i - \frac{i}{μ}) = ti (\frac{μ - 1}{μ}) \\ \begin{matrix} i = θ \\ μ = n \end{matrix} i.e. x = \frac{t θ (n - 1)}{n} \end{array}$

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