Question

A convex lens of focal length f₁ is kept in contact with a concave lens of focal length f₂. Find the focal length of the combination.

Answer 1

 

For convex lens of focal length (+ f₁)

+ 1/f₁ = 1/v' - 1/u     (1)

For concave lens of focal length (– f₂)

- 1/f₂ = 1/v - 1/v'   (2)

Adding equation (1) and (2)

1/f₁ - 1/f₂ = 1/v - 1/u     (3)

For an equivalent lens (using lens formula) 1/f = 1/v - 1/u,where f is the focal length of combination.                 (4)
From equation (3) and (4),

1/f = 1/f₁ - 1/f₂