Question

A ray of light is incident on one face of a transparent slab of thickness 15 cm. The angle of incidence is 60${}^o$. If the lateral displacement of the ray on emerging from the parallel plane is 5$\sqrt{3}$ cm, the refractive index of the material of the slab is

• A. 1.414
• B. 1.532
• C. 1.732
• D. none

Answer 1

Answer: (C)

1.732

The formula for lateral displacement through a glass slab is given by,
$x=\frac{t\times sin(i-r)}{cosr}$

Substituting the values, we get the angle of refraction, $r={30}^o$

Thus, the refractive index of the material is given by, $\mu =\frac{sini}{sinr}$

Hence, $\mu =\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}$

Thus, $\mu =\sqrt{3}=1.732$