Question

A certain prism is that to produce minimum deviation of 38${}^{\circ }.$ It produces a deviation of 44${}^{\circ }$when the angle of incidence is either 42${}^{\circ }$ or 62${}^{\circ }.$The refractive index of material of prism is

• A. 1.51
• B. 1.33
• C. 1.62
• D. 1.732

Answer 1

Answer: (A)

1.51

${\delta }_m={38}^{\circ }$

$r_1+r_2=A$

$\delta =(i_1+i_2-A)$

$\delta ={44}^{\circ }$ $i={62}^0$ or ${42}^{\circ }$

$\mu =?$

$r_1=r_2\Rightarrow r=A/2$

$i=\frac{A+\delta m}{2}$

$\mu =\frac{sin\left(\frac{A+{\delta }_m}{2}\right)}{sinA/2}$

$44=(62+42)-A$

$A={60}^{\circ }$

$\mu =\frac{sin\left(\frac{60+{38}^{\circ }}{2}\right)}{sin\left(30\right)}$

$=2\times .754=1.51$