First slide

Ray optics

Question

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

Easy

A

$3 \times 10^{8} m / s$
B

$1.5 \times 10^{8} m / s$
C

$\frac{3}{\sqrt{2}} x 10^{8} m / s$
D

$\sqrt{2} x 10^{8} m / s$

Solution

$\begin{array}{l} \sin C = \frac{1}{μ} \\ \sin 45^{\circ} = \frac{1}{μ} \\ \frac{1}{\sqrt{2}} = \frac{1}{μ} \\ μ = \sqrt{2} \end{array}$
Velocity of light in medium
$\begin{array}{l} v = \frac{c}{μ} \\ v = \frac{3 \times 10^{8}}{\sqrt{2}} m / s \end{array}$

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