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Physics · 2024 · 2 marks
CBSE 2024 · Region 4 · Set 1 · Q19
A ray of light is incident normally on one face of an equilateral glass prism of refractive index μ. When the prism is completely immersed in a…
A ray of light is incident normally on one face of an equilateral glass prism of refractive index $\displaystyle \mu$. When the prism is completely immersed in a transparent medium, it is observed that the emergent ray just grazes the adjacent face. Find the refractive index of the medium.
Marking-scheme solution
From Snell's law: $\displaystyle \mu \sin i=\mu_{m} \sin r$
$\displaystyle \mu \sin 60^{\circ}=\mu_{m} \sin 90^{\circ}$
$\displaystyle \mu_{m}=\mu \cdot \frac{\sqrt{3}}{2}$
OR
$\displaystyle \mu=\frac{1}{\sin C}$
$\displaystyle \frac{\mu}{\mu_{m}}=\frac{1}{\sin 60^{\circ}}$
$\displaystyle \mu_{m}=\frac{\sqrt{3}}{2} \mu$
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