Question

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index :

• A. lies between $\sqrt{2}$ and $1$
• B. lies between 2 and $\sqrt{2}$
• C. is less then 1
• D. is greater then 2

Answer 1

Answer: (B)

The angle of minimum deviation is given as
${\delta }_{\min }=i+e-A$
for minimum deviation
${\delta }_{\min }=A$ then
$2A=i+e$
in case of ${\delta }_{\min };i=e$
$2A=2i{r}_1=r_2=\frac{A}{2}$
$i=A=90^{\circ }$
$1\sin r=n\sin r_1$
$\sin A=n\sin \frac{A}{2}$
$2\sin \frac{A}{2}\cos \frac{A}{2}=n\sin \frac{A}{2}$
$2\cos \frac{A}{2}=n$
when $A=90^{\circ }=i_{\min }$
then $n_{\min }=\sqrt{2}$
$i=A=0$
$n_{\max }=2$