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Physics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 3 · Q21
A ray of light is incident at an angle 2A on one of the faces of a glass prism of refracting angle A. After refraction from this face, the ray…
A ray of light is incident at an angle 2A on one of the faces of a glass prism of refracting angle A. After refraction from this face, the ray strikes the opposite face which is silvered. The reflected ray from this face retraces on its path. Trace the ray diagram and find the relation between the refractive index of material of prism and the angle of prism.
Marking-scheme solution
From Snell's law: $\displaystyle n_{1} \cdot \sin i=n_{2} \cdot \sin r$
$\displaystyle \mathrm{A}=r_{1}+r_{2}$
$\displaystyle \mathrm{A}=r_{1}$ ($\displaystyle \because r_{2}=0$, the ray retraces its path)
$\displaystyle 1 \times \sin 2 \mathrm{~A}=n \times \sin \mathrm{A}$
$\displaystyle 2 \sin \mathrm{A} \cos \mathrm{A}=n \times \sin \mathrm{A}$
$\displaystyle n=2 \cos \mathrm{A}$
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