Question

Two thin convex lenses as made of glass are placed in close contact with each other. The focal length of each lens is f. If the space between the lenses is filled with same glass material as shown, then the effective focal length of the system is

• A. f
• B. 2f
• C. 3f
• D. $\frac{3}{2}f$

Answer 1

The correct option is A f

Lenses are kept in contact as shown in figure.

$f_1$ = f
$f_2$ = f
$f_3$ = –f (Since, same material is poured in the space between the two lenses.)
So, equivalent focal length, $f_c$, of the combination will be
$\frac{1}{f_c}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}$$\Rightarrow \frac{1}{f_c}=\frac{1}{f}+\frac{1}{f}+\frac{1}{f}$$\Rightarrow \frac{1}{f_c}=\frac{1}{f}$$\Rightarrow f_c=f$
Hence, the correct answer is option (a).