First slide

Ray optics

Question

A glass prism has angle of prism $90^{O}$ and a refractive index of 1.5. A ray is incident at an angle of $30^{O} .$ The ray emerges from an adjacent face at an angle of ___

Moderate

A

$60^{O}$
B

$30^{O}$
C

$45^{O}$
D

The ray does not emerge

Solution

$\begin{array}{l} \sin r_{1} = \frac{\sin 30^{0}}{(3 / 2)} = \frac{1}{3} \\ ∴ r_{2} = 90^{0} - \sin^{- 1} (\frac{1}{3}) > 60^{0} \\ N o w, θ_{C} = \sin^{- 1} (\frac{2}{3}) = \sin^{- 1} (0.667) < 60^{0} \\ S i n c e r_{2} > θ_{C}, t o t a l i n t e r n a l r e f l e c t i o n t a k e s p l a c e . \end{array}$

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