A sphere of radius R of material of refractive index mu_3. Where should an object be placed so that a real image is formed equidistant from the sphere?

A sphere of radius R of material of refractive index mu_3. Where shoul

1.	A sphere of radius R of material of refractive index mu_3. Where should an object be placed so that a real image is formed equidistant from the sphere?
Answer» Solution :Let object be placed ata distance x from the pole `P_1` of the sphere then the ray must pass symmetrically through the sphere, as shown in the FIGURE. Applying the EQUATION at the first surface, we get `mu_2/(- infty)-mu_1/(-x)= (mu_2-mu_1)/(-R) or x=(mu_1/(mu_2-mu_1)) R` Note that the real IMAGE is formed only when the refractive index of the sphere is more than that of the surrounding i.e, `mu_2 GT mu_1`.