Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsRefraction at plane surfaceMedium2 minQB

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Passage / Comprehension

The angle of incidence for a light ray is $θ_{1} = 2 0^{\circ}$ , and the angle of refraction for the refracted ray is $θ_{r} > 2 0^{\circ}$ .

If the angle of incidence is decreased by 10°, then the angle of refraction

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Answer:

Solution:

By Snell's law, $n_{1} sin θ_{1} = n_{2} sin θ_{r} \Rightarrow \frac{s i n θ _{1}}{s i n θ _{r}} = \frac{n _{2}}{n _{1}} < 1$ , so $sin θ_{r} = k sin θ_{1}$ with $k > 1$ .

Differentiating: $\frac{d θ _{r}}{d θ _{1}} = k \frac{c o s θ _{1}}{c o s θ _{r}}$ . Since $θ_{r} > θ_{1}$ , $cos θ_{r} < cos θ_{1}$ , so this ratio is greater than 1.

$θ_{r}$ decreases by more than $1 0^{\circ}$ .

Stream:JEESubject:PhysicsTopic:Geometrical OpticsSubtopic:Refraction at plane surface

⏱ 2mℹ️ Source: QB

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