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Q. 16

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

FIGURE EX34.16 shows a transparent hemisphere with radiusand index of refraction n. What is the maximum distancefor which a light ray parallel to the axis refracts out through the curved surface?

the maximum distancefor which a light ray parallel to the axis refracts out through the curved surfac

See the step by step solution

Step by Step Solution

Step 1 : Total Internal Reflection

The boundary prevents the ray from refracting. Instead, all of the light reflects back into the prism from the boundary. This is known as total internal reflection, or TIR for short.

Step 2 : Crtical Angle

A critical angle is reached when. Because, Snell’s lawgives the critical angle of incidence as

Step 3 : Determine the maximum distance  for which the light ray refracts out through the curved surface:

A transparent hemisphere having a radius of and a refractive index of n.

A light ray is travelling parallel to the hemisphere's axis.

The critical angle of the hemisphere is found from equation which is the minimum angle for which the light ray refracts out through the curved surface.

wherebecause we imagine the hemisphere is in air andis the hemisphere's refractive index:

Step 4 :

The sine of the critical angleis obtained from the above figure:

Solve for:

where the critical anglerefers to the maximum distancethat the light ray refracts out from the hemisphere's curved surface.

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