Question

Two identical glass (${\mu }_e=3/2$) lenses of focal length f each keeps in contact. The space between the two lenses is filled with water (${\mu }_w=4/3$). The focal length of the combination is.

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

Answer 1

Answer: (A)

$3f/4$

The water in between two convex lenses in contact acts like concave lens.

Focal length of convex lens is given by

$\frac{1}{f}=({\mu }_e-1)\frac{2}{R}=\frac{1}{R}$

Focal length of concave lens is given by

$\frac{1}{f^{\prime }}=-({\mu }_w-1)\frac{2}{R}=-\frac{2}{3f}$

$⟹f^{\prime }=-\frac{3f}{2}$

Equivalent focal length is given by

$P=\frac{1}{f_{eq}}=\frac{1}{f}-\frac{2}{3f}+\frac{1}{f}=\frac{4}{3f}$

$⟹f_{eq}=\frac{3f}{4}$