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  • . The refracting angle of a prism is A and the refractive index of the material of the prism is <img alt="\mathrm{cot(A/2)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7Bcot%28A

. The refracting angle of a prism is A and the refractive index of the material of the prism is \mathrm{cot(A/2)}. The angle of minimum deviation of the prism is:

Option: 1

\mathrm{\pi +2A}


Option: 2

\mathrm{\pi -2A}


Option: 3

\mathrm{\frac{\pi}{2}+A}


Option: 4

\frac{\pi}{2}\mathrm{-A}


Answers (1)

best_answer

\mathrm{\text { Here, } \mu=\cot \left(\frac{A}{2}\right)}
According to prism formula
\mathrm{\mu=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin \left(\frac{A}{2}\right)}}
\begin{aligned} & \cot \left(\frac{A}{2}\right)=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin \left(\frac{A}{2}\right)} \Rightarrow \frac{\cos \left(\frac{A}{2}\right)}{\sin \left(\frac{A}{2}\right)}=\frac{\sin \left(\frac{A+\delta_m}{2}\right)}{\sin \left(\frac{A}{2}\right)} \\ & \cot \left(\frac{A}{2}\right)=\sin \left(\frac{A+\delta_m}{2}\right) \Rightarrow \sin \left(\frac{\pi}{2}-\frac{A}{2}\right)=\sin \left(\frac{A+\delta_m}{2}\right) \end{aligned}
\begin{aligned} &\mathrm{ \frac{\pi}{2}-\frac{A}{2}=\frac{A+\delta_m}{2}} \\ &\mathrm{ \pi-A=A+\delta_m} \end{aligned} \quad \text { or } \quad \delta_m=\pi-2 A

Posted by

himanshu.meshram

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