First slide

Prism

Question

The curve of angle of incidence versus angle of deviation shown has been plotted for prism. The value of refractive index of the equilateral prism used is

Moderate

A

$\sqrt{3}$
B

$\sqrt{2}$
C

$\frac{\sqrt{3}}{\sqrt{2}}$
D

$\frac{2}{\sqrt{3}}$

Solution

$δ = i + e - A, d_{\min} = 60^{0},$ when $i = e$
$∴ 60^{0} = 2 i - A = 2 (60^{0}) - A$
$∴ μ = \frac{\sin (\frac{A + δ_{\min}}{2})}{\sin (\frac{A}{2})} = \frac{\sin (\frac{60 + 60}{2})}{\sin (\frac{60}{2})} = \sqrt{3}$

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