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A light ray passes through a prism of angle A in a position of minimum deviation. Obtain and expression for (a) the angle of incidence in terms of the angle of the prism and the angle of minimum deviation (b) the angle of refraction in terms of the refractive index of the prism. |
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Answer» Solution :In the quadrilateral AQNR `angleA+angleQNR=180^(@)" ………………………..(1)"` From `Delta^("le")` QNR, `r_(1)+r_(2)+angleQNR=180^(@)"………………………..(2)"` `r_(1)+r_(2)=A"………………………………(3)"` `"Total DEVIATION " delta=(i-r_(1))+(e-r_(2))` `delta=i+e-A"....................(4)"` (a) At minimum deviatoin position `delta=D_(m), i=e and r_(1)=r_(2)=r` `THEREFORE"From eq (4), "D_(m)=2i-A` `i=(A+D_(m))/(2)"......................(5)"` (B) From eq (3), `r+r=A` `r=A//2"..........................(6)"` Refractive index of HTE prism `MU=(sini)/(sinr)" ............................(7)"` `sin r=(sini)/(mu), r=sin^(-1)((sini)/(mu))` `mu=(sin((A+D_(m))/(2)))/(sinA//2)".........................(8)"` 
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