Question:
The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index p, of the prism is
The angle of a prism is A. One of its refracting surfaces is silvered. Light rays falling at an angle of incidence 2A on the first surface returns back through the same path after suffering reflection at the silvered surface. The refractive index p, of the prism is
Updated On: Jul 25, 2024
- $ 2 \sin A$
- $ 2 \cos A$
- $ \frac{1}{2} \cos A$
- $\tan A$
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The Correct Option is B
Solution and Explanation
On reflection from the silvered surface, the incident ray will retrace its path, if it falls normally on the surface.
By geometry, r = A
Applying Snell's law at surface PQ,
$ I sin i = \mu sin r $
$\mu = \frac{ sin i}{ sin r } = \frac{ sin 2A}{ sin A } = 2cos A $
By geometry, r = A
Applying Snell's law at surface PQ,
$ I sin i = \mu sin r $
$\mu = \frac{ sin i}{ sin r } = \frac{ sin 2A}{ sin A } = 2cos A $
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Concepts Used:
Reflection of Light
When a light ray falls on any object, it is bounced back from the object. This process is known as the Reflection of light. The light reflected from the object falls into our eyes, making the object visible to us. All the things we see around us are because of reflection.
The reflection of light depends on the type of object. A polished or smooth surface reflects most of the light falling on it, while a rough surface absorbs some amount of light and reflects back the rest of the light. The direction of reflected rays depends upon the surface of the object.