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  4. A prism of refracting angle 60° is made with a material of refractive index μ .For a certain wavelength of light, the angle of minimum deviation is 30° . For this wavelength, the value of u. of material is:

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Q. A prism of refracting angle $ 60{}^\circ $ is made with a material of refractive index $ \mu $ .For a certain wavelength of light, the angle of minimum deviation is $ 30{}^\circ $ . For this wavelength, the value of u. of material is:

EAMCETEAMCET 1996

Solution:

The value of refractive index of material of prism is $ \mu =\frac{\sin \frac{A+{{\delta }_{m}}}{2}}{\sin \frac{A}{2}} $ $ \left( \begin{align} & \text{Given:}\,{{\delta }_{m}}={{30}^{o}} \\ & A={{60}^{o}} \\ \end{align} \right) $ $ \mu =\frac{\sin \left( \frac{{{60}^{o}}+{{30}^{o}}}{2} \right)}{\sin \frac{{{60}^{o}}}{2}} $ $ =\frac{\sin {{45}^{o}}}{\sin {{30}^{o}}} $ $ =\frac{1}{\sqrt{2}}\times \frac{2}{1} $ $ =\sqrt{2}=1.414 $