Question 321: Ray Optics

Question

The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is

Accepted Answer

As $\mu $ = ${{\sin \left( {{{A + \delta } \over 2}} \right)} \over {\sin \left( {{A \over 2}} \right)}}$
$ \Rightarrow $ $\cot {A \over 2}$ = ${{\sin \left( {{{A + \delta } \over 2}} \right)} \over {\sin \left( {{A \over 2}} \right)}}$
$ \Rightarrow $ ${{\cos {A \over 2}} \over {\sin {A \over 2}}} = {{\sin \left( {{{A + \delta } \over 2}} \right)} \over {\sin \left( {{A \over 2}} \right)}}$
$ \Rightarrow $ ${sin\left( {{\pi  \over 2} - {A \over 2}} \right) = \sin \left( {{{A + \delta } \over 2}} \right)}$
$ \Rightarrow $ ${{\pi  \over 2} - {A \over 2}}$ = ${{A \over 2} + {\delta  \over 2}}$
$ \Rightarrow $ $\delta $ = 180
o
- 2A

Answer

90
o
$-$ A

Answer

180
o
+ 2A

Answer

180
o
$-$ 3A

Answer

180
o
$-$ 2A

Ray Optics

The refracting angle of a prism is A, and refractive index of the material of the prism is cot (A/2). The angle of minimum deviation is

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