First slide

Ray optics

Question

Number of waves in a length l traversed by a mono chromatic light in vacuum is 10⁶. When the same length of path is traversed by the same light in a medium other than vacuum, number of waves is $\sqrt{3} \times 10^{6}$ . When the same light travelling in vacuum, strikes the vacuum-medium interface at an angle of incidence 60^o, after refraction, the ray will deviate through an angle of

Moderate

A

30^o
B

45^o
C

15^o
D

25^o

Solution

In vacuum, $l = n_{1} λ$ ,
In the medium, $μ l = n_{2} λ$
$∴ μ = \frac{n_{2}}{n_{1}} = \frac{\sqrt{3} \times 10^{6}}{10^{6}} = \sqrt{3}$
Now $\sin r = \frac{\sin i}{μ} = \frac{\sin 60^{o}}{\sqrt{3}} = \frac{1}{2} \Rightarrow r = 30^{o}$
$∴ δ = i - r = 60^{o} - 30^{o} = 30^{o}$

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