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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Geometrical Optics

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Geometrical Optics

A point source is located at a depth h beneath the surface of water...

A point source is located at a depth hh beneath the surface of water (refractive index =μ= \mu). Identify the shape of the area on the water surface through which light escapes, along with the position of its centre.

Options

  1. AA circular area with its centre directly above the point source
  2. BA rectangular area with its centre directly above the point source
  3. CA circular area whose centre is shifted horizontally by a distance hh
  4. DAn elliptical area with its centre directly above the point source

Correct answer

A. A circular area with its centre directly above the point source

Step-by-step solution

Light rays from the point source at depth hh will escape the water surface if their angle of incidence at the water-air interface is less than or equal to the critical angle θc\theta_c.

The critical angle is given by sin⁡θc=1μ\sin \theta_c = \dfrac{1}{\mu}.

By symmetry, the locus of all points on the surface where the angle of incidence is exactly θc\theta_c is a circle.

The radius of this circle is r=htan⁡θc=hμ2−1r = h \tan \theta_c = \dfrac{h}{\sqrt{\mu^2 - 1}}.

Thus, the light escapes through a circular area on the water surface.

The centre of this circular area lies directly above the point source.
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