a hemisphere (μ=3) of radius placed on a horizontal surface with its base touching the surface .A vertical beam of cross sectional radius (√3/2)r is incident symmetrically on its curved surface.find radius of the spot of light formed on the horizontal surface??????

Dear Abhishiek,

We know that For hemissherical surface

f = R/(n-1) and refractive  n= 3 here

and Magnification is given by M= -S2/S1= f/ f-S1 and S2 is on the other side i.e., on the ground we would get +ve otherwise it would have been -ve

By substituting S1= (√3/2)R

We get S2= S1/(√3-1) Where S1= (√3/2)R

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