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Physics · 2026 · 2 marks
CBSE 2026 · Region 2 · Set 2 · Q19
A ray of light is incident on the face of a triangular prism of refracting angle 60° and it just suffers total internal reflection at the other face.…
A ray of light is incident on the face of a triangular prism of refracting angle $\displaystyle 60$° and it just suffers total internal reflection at the other face. Find the angle of incidence for the ray if the refractive index of the material of the prism is $\displaystyle \sqrt{2}$.
Marking-scheme solution
$\displaystyle \sqrt{2}\left(\sin i_{c}\right)=1$
$\displaystyle \sin i_{c}=\dfrac{1}{\sqrt{2}}$, so $\displaystyle i_{c}=45^{\circ}$
$\displaystyle r_{1}+r_{2}=\mathrm{A}$ (here $\displaystyle r_{2}=i_{c}$)
$\displaystyle r_{1}=\mathrm{A}-i_{c}=60^{\circ}-45^{\circ}=15^{\circ}$
$\displaystyle \sin i=\sqrt{2} \sin 15^{\circ}$
$\displaystyle i=\sin ^{-1}\left[\sqrt{2} \sin 15^{\circ}\right]=\sin ^{-1}(0.366)$
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