If the critical angle for total internal reflection from a medium to vacuum is 45°, then velocity of light in the medium is,

Question

If the critical angle for total internal reflection from a medium to vacuum is 45°, then velocity of light in the medium is, (A) 1.5 × 108 m/s (B) (3/√2)×108 m/s (C) √2×108 m/s (D) 3 × 108 m/s

Tardigrade Admin · Accepted Answer

sin θC=(1/μ) μ=(1/sin θc) =(1/sin 45°) =(1/(1/√2))=√2 μ=(C/V) ⇒ V =(C/μ) =(3×108/√2) m/ sec

Q. If the critical angle for total internal reflection from a medium to vacuum is $4 5^{\circ}$ , then velocity of light in the medium is,

$1.5 \times 1 0^{8} m / s$

$\frac{3}{2} \times 1 0^{8} m / s$

$2 \times 1 0^{8} m / s$

$3 \times 1 0^{8} m / s$

$s in θ_{C} = \frac{1}{μ}$
$μ = \frac{1}{s in θ _{c}}$
$= \frac{1}{s in 4 5 ^{\circ}}$
$= \frac{1}{( 1/ 2 )} = 2$
$μ = \frac{C}{V} \Rightarrow V = \frac{C}{μ}$
$= \frac{3 \times 1 0 ^{8}}{2} m / sec$

Q. If the critical angle for total internal reflection from a medium to vacuum is 45∘, then velocity of light in the medium is,

1.5×108m/s

2​3​×108m/s

2​×108m/s

3×108m/s