Question

A converging lens of focal length 30 cm is placed in contact with another converging lens of unknown focal length, then possible value for focal length of combination is

• A. 15 cm
• B. 60 cm
• C. 36 cm
• D. -12 cm

Answer 1

The correct option is A 15 cm

Given $f_1=30cm$

Since it is a converging lens $f_2$ should be positive.

Equivalent lens is given as

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

$\therefore f=\frac{1}{\frac{1}{f_1}+\frac{1}{f_2}}=\frac{1}{x}$ (say)

Where $x=\frac{1}{f_1}+\frac{1}{f_2}=\frac{1}{30}+\frac{1}{f_2}$

Since $f_2$ is positive we can say that,

$x>\frac{1}{30}=\frac{1}{x}<30$

Also $f=\frac{1}{x}$

Hence $f<30$ and $f$ is positive since it is a setup of converging lenses.

Hence the correct answer is option (A) $15cm$.