Question

Two identical lenses made of the same material of refractive index $1.5$ have thw focal length kept in contact and immersed in a liquid of refractive index $1.35$. The combination behaves as

• A. Convex lens of focal length $27cm$.
• B. Convex lens of focal length $6cm$.
• C. Convex lens of focal length $9cm$.
• D. Convex lens of focal length $16cm$.

Answer 1

The correct option is A Convex lens of focal length $27cm$.

Two identical lenses made of the mass material of refractive index $=1.5$ focal length kept in contact and immersed in a liquid of refractive index $=1.35$

The combination behaves s-

Explanation

$f_1=f_2=12cm$

when lenses are kept in water

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\frac{1}{f}=\frac{1}{12}+\frac{1}{12}\frac{1}{f}=\frac{2}{12}=\frac{1}{6}f=6cm$

Using lens makers formula

$\frac{1}{f}=(n-1)(\frac{1}{R_1}-\frac{1}{R_2})\frac{1}{6}=(\frac{3}{2}-1)(\frac{1}{R_1}-\frac{1}{R_2})=\frac{1}{R_1}-\frac{1}{R_2}=\frac{1}{3}$

Now in liquid

$\frac{1}{f}=(\frac{1.5}{1.35}-1)(\frac{1}{R_1}-\frac{1}{R_2})\frac{1}{f}=0.11\times \frac{1}{3}f=27cm$