A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45°. For which of the following value of μ the ray can undergo total internal reflection?

Question

A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45°. For which of the following value of μ the ray can undergo total internal reflection? (A) μ =1.33 (B) μ =1.40 (C) μ =1.50 (D) μ =1.25

Tardigrade Admin · Accepted Answer

For total internal reflection, sin i > sin c where, i = angle of incidence, C = critical angle But, sin C =(1/μ) ∴ sin i =(1/μ) or μ=(1/ sin i ) .∴ μ>(1/ sin 45) text or μ>√2 text (i = 45 text Given )

Q. A ray of light travelling in a transparent medium of refractive index $μ$ , falls on a surface separating the medium from air at an angle of incidence of $4 5^{\circ}$ . For which of the following value of $μ$ the ray can undergo total internal reflection?

$μ = 1.33$

$μ = 1.40$

$μ = 1.50$

$μ = 1.25$

For total internal reflection, $sin i > sin c$ where, $i =$ angle of incidence, $C =$ critical angle
But, $sin C = \frac{1}{μ} ∴ sin i = \frac{1}{μ}$ or $μ = \frac{1}{s i n i}$
$∴ μ > \frac{1}{s i n 45} or μ > 2 (i = 45 Given)$

Q. A ray of light travelling in a transparent medium of refractive index μ, falls on a surface separating the medium from air at an angle of incidence of 45∘. For which of the following value of μ the ray can undergo total internal reflection?

μ=1.33

μ=1.40

μ=1.50

μ=1.25