A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if θ=45°. The index of refraction of glass is

Question

A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if θ=45°. The index of refraction of glass is (A) Less than 1.41 (B) Equal to 1.41 (C) Greater than 1.41 (D) None of the above

Tardigrade Admin · Accepted Answer

For total internal reflection θ > C ⇒ sin θ > sin C ⇒ sin θ > (1/μ) or μ>(1/ sin θ) ⇒ μ > (1/ sin 45°) ⇒ μ>√2 ⇒ μ > 1.41

Q. A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if $θ = 4 5^{\circ}$ . The index of refraction of glass is

Less than 1.41

Equal to 1.41

Greater than 1.41

None of the above

For total internal reflection $θ > C$
$\Rightarrow sin θ > sin C \Rightarrow sin θ > \frac{1}{μ}$
or $μ > \frac{1}{s i n θ}$
$\Rightarrow μ > \frac{1}{s i n 4 5 ^{\circ}}$
$\Rightarrow μ > 2$
$\Rightarrow μ > 1.41$

Q. A triangular prism of glass is shown in the figure. A ray incident normally to one face is totally reflected, if θ=45∘. The index of refraction of glass is