question_answer

At what angle, a ray of light will incident on one face of an equilateral prism, so that the emergent ray may graze the second surface of the prism (\[\mu \] =1.5)?

A) \[38{}^\circ \]

B) \[82{}^\circ \]

C) \[28{}^\circ \]                  

D) \[48{}^\circ \]

Correct Answer: C

Solution :

Key Idea: Maximum deviation occurs when there is grazing incidence. Since, the prism is an equilateral one, its angles are \[{{60}^{o}}\] each. Maximum deviation occurs when there is grazing incidence, that is, angle of incidence is \[{{90}^{o}}\] From Snell?s law \[\mu =\frac{\sin i}{\sin r}\Rightarrow 1.5=\frac{\sin {{90}^{o}}}{\sin r}\] \[\Rightarrow \] \[\sin \,r=\,\frac{1}{1.5}=0.67\] \[\Rightarrow \]\[r=si{{n}^{-1}}(0.67)={{42}^{o}}\] Also, \[r+r'=A={{60}^{o}}\] \[\Rightarrow \]    \[r'={{60}^{o}}-r\]         \[={{60}^{o}}-{{42}^{o}}={{18}^{o}}\] Let the angle of emergence be i?. Then       \[\frac{\sin i'}{\sin r'}=\mu =1.5\] \[\sin i'=1.5sin{{18}^{o}}=1.5\times 0.31=0.465\] \[\therefore \]    \[i'={{\sin }^{-1}}(0.465)={{28}^{o}}\]