Question

Two plano-concave lenses $(1$ and $2)$ of glass of refractive index $1.5$ have radii of curvature $25cm$ and $20cm$. They are placed in contact with their curved surface towards each other and the space between them is filled with liquid of refractive index $4/3$. Then the combination is

• A. convex lens of focal length 70 cm
• B. concave lens of focal length 70 cm
• C. concave lens of focal length 66.6 cm
• D. convex lens of focal length 66.6 cm

Answer 1

Answer: (C)

$\frac{1}{f_1}=\left(\frac{3}{2}-1\right)\left(\frac{1}{\infty }-\frac{1}{25}\right)=-\frac{1}{50}$
$\frac{1}{f_2}=\left(\frac{4}{3}-1\right)\left(\frac{1}{25}+\frac{1}{20}\right)=\frac{3}{100}$
and $\frac{1}{f_3}=\left(\frac{3}{2}-1\right)\left(\frac{1}{-20}-\frac{1}{\infty }\right)=-\frac{1}{40}$
Now $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$
$=-\frac{1}{50}+\frac{3}{100}-\frac{1}{40}$
$\therefore f=-66.6cm$