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A mark on the surface of a glass spehre ...

A mark on the surface of a glass spehre `(mu=1.5)` is viewed from a diametrically opposite position. It appears to be at a distance 10 cm from its actual position. The radius of the sphere is

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As the mark is viewed from the diametrically opposite position, refraction takes place at side II of the surface (the mark being on side I as shown)
Here `mu_1=1.5, mu_2=1, u=-2R` using `mu_2/v-mu_1/u=(mu_2-mu_1)/R`
`1/v-(1.5)/((-2R))=(1-1.5)/(-R)`
`therefore 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 in figure. Further it is given that, the image of mark is at a distance 10cm from the object. Hence: `4R=2R+10 therefore R=5cm`
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