Question

An equiconvex lens of focal length 15 cm is cut into two equal plano-convex halves. The focal length of each half will be ______.

Options

• 30 cm

• 20 cm

• 15 cm

• 7.5 cm

Answer 1

An equiconvex lens of focal length 15 cm is cut into two equal plano-convex halves. The focal length of each half will be 30 cm.

Explanation:

Using the lens maker’s formula:

`1/f = (mu - 1)(1/R_1 - 1/R_2)`

For an equiconvex lens:

R₁ = R,

R₂ = −R

Focal length of the original lens

`1/f = (mu - 1)(1/R - (-1)/R)`

= `(mu - 1)(2/R)`

f = 15 cm   ...(Given)

`1/15 = (mu - 1)(2/R)`

For plano-convex lens:

R₁ = R

R₂ = ∞

`1/(f') = (mu - 1)(1/R - 0)`

`1/(f') = 1/2  .  1/15`

= `1/30`

f' = 30 cm