First slide

Ray optics

Question

A ray of light is incident on a transparent slab of glass having refractive index $\sqrt{3}$ . A part of incident energy is reflected and the balance amount of energy is refracted into the slab. If the angle between refracted and reflected rays is $90^{o}$ , what is the angle of deviation of the reflected ray?

Moderate

A

$60^{o}$
B

$90^{o}$
C

$150^{o}$
D

$120^{o}$

Solution

$i + r = 90^{0} \Rightarrow r = 90^{0} - i$
$\begin{array}{l} ∴ μ = \frac{\sin i}{\sin r} = \frac{\sin i}{\sin (90^{0} - i)} = \tan i \\ \Rightarrow i = \tan^{- 1} μ = \tan^{- 1} \sqrt{3} = 60^{0} \end{array}$
$∴$ Angle of deviation of reflected ray $= 180^{0} - 2 i = 180^{0} - 2 \times 60^{0} = 60^{0}$

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