Question

A layer of fluid of refractive index $\frac{4}{3}$ is filled between two identical plano convex lens of focal length 30 cm each and refractive index 1.5 as shown in figure, then

• A. Combination behaves as convex lens
• B. Combination behaves as concave lens
• C. Focal length of combination is 45 cm
• D. Focal length of combination is -25 cm

Answer 1

Answer: (A), (C)

The correct options are
A Combination behaves as convex lens
C Focal length of combination is 45 cm


Using lens makers formula,
$\frac{1}{f}=(\mu -1)\frac{1}{R}\Rightarrow \frac{1}{30}=(1.5-1)\frac{1}{R}\Rightarrow R=15cm$


$\frac{1}{f^{\prime }}=(\mu -1)\frac{2}{R}\Rightarrow \frac{1}{f^{\prime }}=-(\frac{4}{3}-1)\times \frac{2}{15}\Rightarrow f^{\prime }=-\frac{45}{2}$

$\frac{1}{f_{eq}}=\frac{1}{f}+\frac{1}{f}+\frac{1}{f^{{}^{\prime }}}=\frac{2}{30}-\frac{2}{45}\Rightarrow f_{eq}=45cm$

Equivalent focal length turned out to be positive, so the lens is converging lens like a convex lens.