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 than $2$
• D. Is greater than $2$

Answer 1

The correct option is B Lies between $2$ and $\sqrt{2}$

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 $n_{min}=\sqrt{2}$
$i=A=0$

$n_{max}=2$.