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A ray of light is refracted through a sphere whose material has a refractive index mu in such a way that it passes through the extremities of two radii which make an angle beta with each other. Prove that if alpha is the deviation of the ray caused by its passage through the sphere, then cos((beta-alpha)/2)=mu cos(beta/alpha) |
Answer»  `:. alpha=(i-r)+(i-r)` `or i-r=alpha/2….(i)` Further, in `angleOPQ, r+r+beta=180^@` `:. r=90^@-beta/2…..(ii)` From EQ.(i), `i=r+alpha/2=90^@+((alpha-beta)/2).....(III)` `mu=sini/sinr=(SIN[90^@+((alpha-beta)/2)])/(sin(90-beta/2))` `=(COS((beta-alpha)/2))/(cos(beta/alpha))` or `cos((beta-alpha)/2)=mu cos beta/2` Henced proved |
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