Question

A concave lens of focal length 10 cm is cut into two identical plano-concave lenses. The focal length of each lens will be ______.

Options

• 20 cm

• 30 cm

• 40 cm

• 5 cm

Answer 1

A concave lens of focal length 10 cm is cut into two identical plano-concave lenses. The focal length of each lens will be 20 cm.

Explanation:

For a thin concave lens with a focal length (f) of 10 cm, the power (P) is the sum of the powers of its two surfaces. In a symmetric concave lens, each surface contributes equally to the total power:

`1/f = 1/f_1 + 1/f_2`

Given f = 10 cm, and because the parts are identical (f₁ = f₂):

`1/10 = 1/f_1 + 1/f_1`

= `2/f_1`

When the lens is cut vertically, each new plano-concave lens consists of one original curved surface and one new flat (plane) surface. The flat surface has an infinite radius of curvature, meaning it has zero power. Therefore, the focal length of each new part (f_new) is simply the focal length of a single original surface (f₁):

`1/10 = 2/f_"new"`

f_new = 10 × 2

= 20

The power of the lens is halved when it is split this way, which causes the focal length to double. Thus, each plano-concave lens will have a focal length of 20 cm.