question_answer

For the angle of minimum deviation of a prism to be equal to its refracting angle, the prism must be made of a material whose refractive index

A) Lies between \[\sqrt{2}\] and 1

B) Lies between 2 and \[\sqrt{2}\]

C) Is less than 1       

D) Is greater than 2

Correct Answer: B

Solution :

The angle of minimum deviation is given as \[{{\delta }_{\min }}=i+e-A\] for minimum deviation \[{{\delta }_{\min }}=A\] then \[2A=i+e\] in case of \[{{\delta }_{\min }}i=e\] \[2A=2i\]  \[{{r}_{1}}={{r}_{2}}=\frac{A}{2}\] \[i=A=90{}^\circ \] From smell's law \[1\sin i=n\sin {{r}_{1}}\] \[\sin A=n\sin \frac{A}{2}\] \[2\sin \frac{A}{2}\cos \frac{A}{2}=n\sin \frac{A}{2}\] \[2\cos \frac{A}{2}=n\] When \[A=90{}^\circ ={{i}_{\min }}\] Then \[{{n}_{\min }}=\sqrt{2}\] \[i=A=0\,\,{{n}_{\max }}=2.\]