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An isosceles prism has one of the refrac...

An isosceles prism has one of the refracting surfaces silvered. A ray of light is incident normally on the refracting face AB. After two reflections, the ray emerges from the base of the prism perpendicular to it. Find the angle of the prism.

Text Solution

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The incident ray passes without deviation from face AB. It suffers reflections at P and Q. From Fig. , incident ray and normal at Q are parallel, therefore,
`d=2A` (i)
Also, `2alpha+A=180^(@) ` (ii)
On solving Eqs. (i) and (ii), we get `A = 36^(@), alpha=72^(@)`
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