First slide

Total internal reflection - Ray optics and optical instruments

Question

A rectangular block of glass is placed on a printed page lying on a horizontal surface. The minimum value of the refractive index of glass for which the letters on the page are not visible from any of the vertical faces of block is

Moderate

A

$\geq \sqrt{3}$
B

$\geq 1.55$
C

$\geq \sqrt{2}$
D

$\geq 1.38$

Solution

For object not to be visible from vertical face (AC) any ray starting from object should not come
out of vertical face. i.e., suffer TIR at vertical face.
Assume BAC to be prism of angle $A = 90^{0}$ . The condition for no ray to emerge from second
refracting surface of prism is $A \geq 2 C$
$\Rightarrow 90 \geq 2 C$
Or $C \leq 45^{0}$
$\Rightarrow \sin C \leq 1 / \sqrt{2}$
Or $n \geq \sqrt{2}$

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