Question

A prism of material refractive index u has refracting
angle A. For which of the following conditions
will be no emergent light whatever may be
angle of incidence? ​

Answer 1

Answer:

The condition for which there will be no emergent light whatever may be

angle of incidence is

$\mu > cosec(\frac{A}{2})$

Explanation:

Let the light incident on the 2nd surface of prism at angle "r"

If no light come out of the prism then we have

$r > \theta_c$

also we know

$\mu sin\theta_c = 1$

$sin\theta_c = \frac{1}{\mu}$

$\theta_c = sin^{-1}(\frac{1}{\mu})$

now we have

$r > sin^{-1}(\frac{1}{\mu})$

now we know

$r_1 + r_2 = A$

so we have

$r_1 + r = A$

$r_1 = A - r$

also by snell's law at first surface

$1 sin i = \mu sin r_1$

$sin i = \mu sin(A - r)$

now for all range of incidence angle there should not be any emergent ray

so i = 90 degree

$sin(A - r) = \frac{1}{\mu}$

$r = A - sin^{-1}(\frac{1}{\mu})$

now from above equation

$A - sin^{-1}(\frac{1}{\mu}) > sin^{-1}(\frac{1}{\mu})$

$A > 2sin^{-1}(\frac{1}{\mu})$

so we have

$\mu > cosec(\frac{A}{2})$

#Learn

Topic : Prism

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