Question

Rays are incident on a prism at various angles and the $\delta$ vs. $i$ graph obtained is shown in figure below. Find the prism angle and refractive index of material ($sin{40}^0=0.64$).

• A. ${60}^o$, $1.92$
• B. ${30}^o$, $1.28$
• C. ${60}^o$, $1.28$
• D. ${45}^o$, $1.36$

Answer 1

The correct option is C ${60}^o$, $1.28$

$\delta =i+e-A$
${30}^0={37}^0+{53}^0-A$
${30}^0={90}^0-A$
$A$ = ${60}^0$
${\delta }_m=2i-A=2\left({40}^0\right)-{60}^0$
${\delta }_m={20}^0$
$n=\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{sin\left(\frac{A}{2}\right)}=\frac{sin\left(\frac{{60}^0+{\delta }_m}{2}\right)}{sin{30}^0}$
$=\frac{sin\left(\frac{{60}^0+{20}^0}{2}\right)}{sin{30}^o}$
$=\frac{sin{40}^0}{sin{30}^0}$
= 2 $sin{40}^0$ = $1.28$