Physics - Geometrical Optics Question with Solution | TestHub

PhysicsGeometrical OpticsRefraction at curved surface/LensEasy2 minPYQ_2020

PhysicsEasysingle choice

A light beam of diameter $\sqrt{3} R$ is incident symmetrically on a glass hemisphere of radius $R$ and of refractive index $n = \sqrt{3} .$ The radius of the beam at the base of the hemisphere is

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Solution:

From the given ray diagram shown in the figure below $μ_{1} s i n i = μ_{2} s i n r$

$\Rightarrow 1 \times s i n 60 ° = \sqrt{3} \times s i n r$

$\Rightarrow r = 30 °$

In $ΔMNP$

$t a n 30 ° = \frac{x}{(\frac{R}{2})}$

$\Rightarrow x = \frac{R}{2 \sqrt{3}}$

From the geometry of the figure

$\Rightarrow r = \frac{\sqrt{3}}{2} R - x = \frac{\sqrt{3}}{2} R - \frac{R}{2 \sqrt{3}}$

$= (\frac{3 - 1}{2 \sqrt{3}}) R = \frac{R}{\sqrt{3}}$

Subject:PhysicsTopic:Geometrical OpticsSubtopic:Refraction at curved surface/Lens

⏱ 2mℹ️ Source: PYQ_2020

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