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(a) Plot a graph for angle of deviation as a function of angle of incidence for a triangular prism. (b) Derive the relation for the refractive index of the prism in terms of the angle of minimum deviation and angle of prism. |
Answer» Solution :(a)  (b) A Ray PQ is incident on the face AB of prism at an angle I and refrected along QR at angle r. The angle between the EMERGENT ray RS and incident Ray PQ is called angle of deviation. `angleA+angleQNR=180^(@)"....(1)"` `-r+r'=angleQNR=180^(@)"....(2)"` from equation (1) and (2) `A=r+r'"....(3)"` `DELTA=angleMQR+angleMRQ"(exterior angle)"` `delta=(i+r)+(i'-r')` `delta=(i+i')-(r+r')"....(4)"` In the minimum deviation position (when `delta=delta_(m)`) `i=i',""r=r'""....(5)"` `"from (3) and (5)"r=A//2"....(6)"` `"from (4) and (5)" i=(A+delta_(m))/(2)"....(7)"` `mu=(sin i)/(sin r)"(according to SNELL's law)"` Substituting the value of i and r from equation (6) and (7) `mu=(sin i)/(sin r)=(sin""(A+(delta_(m))/(2)))/(sin""(A)/(2))` 
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