Question

For a prism PQR, the incident and emergent rays are parallel as shown in fig. The minimum value of refractive index of the prism material is :

• A. $\sqrt{3}$
• B. 1.5
• C. $\sqrt{2}$
• D. 2

Answer 1

Answer: (C)

$\sqrt{2}$

The minimum value of refractive index means preventing the entering ray from escaping prism,so applying snell's law at the surfaces PQ and QR,

at surface PQ:-

$\angle i={45}^0$

${\mu }_{min}=refractive$ $index$ $of$ $prism$.

For the ray just preventing from getting out of prism:-

$\angle r={90}^0$

$\mu =1$ (for air)

using Snell's Law:

${\mu }_{min}\sin i=\mu \sin r{\mu }_{min}\sin {45}^0=1\times \sin {90}^0$

${\mu }_{min}=\sqrt{2}$