Question

A convex lens of focal length 'f' is placed in contact with a concave lens of the same focal length. The equivalent focal length of the combination is ______.

Options

• ${\displaystyle f}$

• infinity

• ${\displaystyle \frac{f}{2}}$

• zero

Answer 1

A convex lens of focal length 'f' is placed in contact with a concave lens of the same focal length. The equivalent focal length of the combination is infinity.

Explanation:

Given, focal length of convex lens, f₁ = f and focal length of concave lens, f₂ = - f.

The focal length of combination, when two lenses are in contact is given by

${\displaystyle \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}}$  ...(i)

Substituting given value in Eq. (i), we get

${\displaystyle \Rightarrow \frac{1}{f}+\frac{1}{f}-\frac{1}{f}=0\Rightarrow f=\infty }$

Hence, the equivalent focal length of the combination is infinity.