An isosceles prism of angle A=30° has one of its surfaces silvered. Light rays falling at an angle of incidence 60° on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

Question

An isosceles prism of angle A=30° has one of its surfaces silvered. Light rays falling at an angle of incidence 60° on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is (A) 1.414 (B) 1.5 (C) 1.732 (D) 1.866

Tardigrade Admin · Accepted Answer

For light to retrace its path it must reflect normally in the mirror. When it does so, by geometry r=30° μ=( sin i/ sin r)=( sin 60°/ sin 30°)=√3=1.732 <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/756b24b7e2852c80f2d71bef44c6eba2-.png" />

Q. An isosceles prism of angle $A = 3 0^{\circ}$ has one of its surfaces silvered. Light rays falling at an angle of incidence $6 0^{\circ}$ on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

1.414

1.5

1.732

1.866

For light to retrace its path it must reflect normally in the mirror.
When it does so, by geometry $r = 3 0^{\circ}$
$μ = \frac{s i n i}{s i n r} = \frac{s i n 6 0 ^{\circ}}{s i n 3 0 ^{\circ}} = 3 = 1.732$

Q. An isosceles prism of angle A=30∘ has one of its surfaces silvered. Light rays falling at an angle of incidence 60∘ on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

1.414

1.5

1.732

1.866

For light to retrace its path it must reflect normally in the mirror. When it does so, by geometry r=30∘ μ=sinrsini​=sin30∘sin60∘​=3​=1.732

Q. An isosceles prism of angle $A = 3 0^{\circ}$ has one of its surfaces silvered. Light rays falling at an angle of incidence $6 0^{\circ}$ on the other surface retrace their path after reflection from the silvered surface. The refractive index of prism material is

For light to retrace its path it must reflect normally in the mirror.
When it does so, by geometry $r = 3 0^{\circ}$
$μ = \frac{s i n i}{s i n r} = \frac{s i n 6 0 ^{\circ}}{s i n 3 0 ^{\circ}} = 3 = 1.732$