The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is

Question

The refractive index of the material of a prism is √2 and the angle of the prism is 30°. One of the two refracting surfaces of the prism is made a mirror inwards, by silver coating. A beam of monochromatic light entering the prism from the other face will retrace its path (after reflection from the silvered surface) if its angle of incidence on the prism is (A) zero (B) 60° (C) 30° (D) 45°

Tardigrade Admin · Accepted Answer

For retracing its path, light ray should be normally incident on silvered face.

Applying Snell's law at

M

,

\frac{s i n i}{s i n 3 0 ^{\circ}} = \frac{2}{1}

\Rightarrow sin i = 2 \times \frac{1}{2}

sin i = \frac{1}{2}

i.e.

i = 4 5^{\circ}

zero

$6 0^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

For retracing its path, light ray should be normally incident on silvered face.

Applying Snell's law at $M$ ,
$\frac{s i n i}{s i n 3 0 ^{\circ}} = \frac{2}{1}$
$\Rightarrow sin i = 2 \times \frac{1}{2}$
$sin i = \frac{1}{2}$
i.e. $i = 4 5^{\circ}$

zero

60∘

30∘

45∘

For retracing its path, light ray should be normally incident on silvered face. Applying Snell's law at M, sin30∘sini​=12​​ ⇒sini=2​×21​ sini=2​1​ i.e. i=45∘

$6 0^{\circ}$

$3 0^{\circ}$

$4 5^{\circ}$

For retracing its path, light ray should be normally incident on silvered face.

Applying Snell's law at $M$ ,
$\frac{s i n i}{s i n 3 0 ^{\circ}} = \frac{2}{1}$
$\Rightarrow sin i = 2 \times \frac{1}{2}$
$sin i = \frac{1}{2}$
i.e. $i = 4 5^{\circ}$