Question

A telescope system consists of two glass balls with radii R₁ = 5.0 cm and R₂ = 1.0 cm. What are the distance between the centres of the balls and the magnification of the system if the bigger ball serves as an objective?

Answer 1

Let the optical powers of the first and second surfaces of the ball of radius R₁ be Φ'₁ and Φ₂" then

This ball may be treated as a thick spherical lens of thickness 2R₁ So the optical power of this sphere is, 

If the distance between the centres of these balls bed. Then the optical power of whole system,

Now, since this system serves as telescope, the optical power of the system must be equal to zero.

Since the diameter D of the objective is 2R and that of the eye-piece is d = 2R₁ So, the magnification,