Ray Optics

JEE Main level, numerical answer, medium

250 of 295

Question 250 of 295

The refractive index of a transparent liquid filled in an equilateral hollow prism is 2\sqrt{2}. The angle of minimum deviation for the liquid will be _______∘^{\circ}.

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Answer: 30

For minimum deviation in a prism,
μ=sin⁡(Dmin+A2)sin⁡A2\mu =\dfrac{\sin \left(\dfrac{{D}_{min}+A}{2}\right)}{\sin \dfrac{A}{2}}
The value of minimum deviation is
⇒2=sin⁡(Dmin+60∘2)sin⁡30∘\Rightarrow \sqrt{2}=\dfrac{\sin \left(\dfrac{{D}_{min}+60^{\circ}}{2}\right)}{\sin 30^{\circ}}
⇒12=sin⁡(Dmin+60∘2)⇒45∘=(Dmin+60∘2)⇒Dmin=30∘\Rightarrow \dfrac{1}{\sqrt{2}}=\sin \left(\dfrac{{D}_{min}+60^{\circ}}{2}\right) \Rightarrow 45^{\circ}=\left(\dfrac{{D}_{min}+60^{\circ}}{2}\right) \Rightarrow {D}_{min}=30^{\circ}

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