Question

Two identical glass $(\mu_g = 3/2)$ equiconvex lenses of focal length $f$ each are kept in contact. The space between the two lenses is filled with water $(\mu_w = 4/3)$. The focal length of the combination is

• A. $f/3$
• B. $f$
• C. $4f/3$
• D. $3f/4$

Answer 1

Answer: (D)

$3f/4$

Answer 2

For equiconvex lens
$\frac{1}{A} = \left(\frac{3}{2} -1 \right) \left(\frac{1}{R} - \frac{1}{-R}\right)$
$\frac{1}{f } = \frac{1}{2} . \frac{2}{R}$
$R =f$
For $2^{nd}$ lens $\frac{1}{f_{2}} = \left(\frac{4}{3} -1\right) \left(\frac{1}{-f} - \frac{1}{-f}\right)$
$\frac{1}{f_{2} } = \frac{1}{3} \times\frac{2}{-f}$
$f_{2} = \frac{-3 f}{2}$
For combination
$\frac{1}{f'} = \frac{1}{f_{1}} + \frac{1}{f_{2}} + \frac{1}{f_{3}}$
$= \frac{1}{f} + \frac{2}{-3 f} + \frac{1}{f}$
$\frac{1}{f'} = \frac{3-2+3}{3f} = \frac{4}{3f}$
$f' = \frac{3f}{4}$