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 \[{{n}_{\min }}=\sqrt{2}\] \[i=A=0\,\,{{n}_{\max }}=2.\]You need to login to perform this action.
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