# A ray of light passes through a prism of refractive index √2 as shown in the figure. Find:

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A ray of light passes through a prism of refractive index √2 as shown in the figure. Find:

(i) The angle of minimum deviation for this prism.

(ii) the angle of incidence ($\angle r_2$) at face AC.

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(i) The angle of minimum deviation

$x = \frac{sin{\left(\frac{A+S_m}{2}\right)}}{sin\left(\frac A2\right)}$

$\sqrt2=\frac{sin\left(\frac{60 + S_m}{2}\right)}{sin\left(\frac{60}2\right)}$

$\sqrt2 \,sin\,30^\circ = sin\left(\frac{60^\circ+S_m}{2}\right)$

$\sqrt2 \times\frac12= sin\left(\frac{60^\circ+S_m}{2}\right)$

$\frac1{\sqrt2}= sin\left(\frac{60^\circ+S_m}{2}\right)$

$sin^{-1}\left(\frac1{\sqrt2}\right)= \frac{60^\circ+S_m}{2}$

$45^\circ= \frac{60^\circ+S_m}{2}$

$90^\circ= {60^\circ+S_m}$

$S_m = 30^\circ$

(ii) Angle of incidence

$i = \frac{A+S_m}{2}$

$i = \frac{60^\circ+30^\circ}{2}$

$i = 45^\circ$