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A small object stuck on the surface of a...

A small object stuck on the surface of a glass sphere `(n=1.5)` is viewed from the diametrically opposite position. Find transverse magnification.

Text Solution

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Refraction will take place at side II on the surface.
`mu_2/v-mu_1/mu= (mu_2-mu_1)/R`
Here `mu_1=1.5 mu_2=1`
and u=-2R
`1/v-1.5/((-2R))=(1-1.5)/(-R) implies 1/v=0.5/R-1.5/(2R)=(-0.5)/(2R) or v=-4R`
negative sign indicates that the image is formed to the left of refracting surface as shown. Magnification.
`m=(mu_1v)/(mu_2v)=(1.5(-4R))/(1(-2R)) therefore m=3ans`
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