Ray Optics

JEE Main level, numerical answer, medium

243 of 295

Question 243 of 295

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60∘60^{\circ}. The refractive index of the prism material is 2\sqrt{2}. The angle of incidence (in degrees) is ______.

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Answer: 45

μ=sin⁡(A+δm2)sin⁡(A2), since A=60∘∴δm=30∘δm=2i−A[ as i=e]⇒i=45∘\begin{aligned} & \mu=\frac{\sin \left(\frac{\mathrm{A}+\delta_{\mathrm{m}}}{2}\right)}{\sin \left(\frac{\mathrm{A}}{2}\right)}, \text { since } \mathrm{A}=60^{\circ} \quad \therefore \delta \mathrm{m}=30^{\circ} \\ & \delta_{\mathrm{m}}=2 \mathrm{i}-\mathrm{A}[\text { as } \mathrm{i}=\mathrm{e}] \\ & \Rightarrow \mathrm{i}=45^{\circ}\end{aligned}

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