A mark on the surface of a glass sphere is viewed froma diametrically opposite position. It appears to be at a distance 10cm from its actual position Find the radius of sphere.

A mark on the surface of a glass sphere is viewed froma diametrically

1.	A mark on the surface of a glass sphere is viewed froma diametrically opposite position. It appears to be at a distance 10cm from its actual position Find the radius of sphere.
Answer» Solution :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`