Question

Achromatic combination of lenses comprises of the two lenses of same material placed $4cm$ apart. If focal length of one lens is $5cm,$ the focal length of other lens is:

• A. $2cm$
• B. $4cm$
• C. $6cm$
• D. $3cm$

Answer 1

The correct option is D $3cm$

$\frac{W_1}{W_2}=\frac{-f_1}{f_2}$

both are as same material $\left(W_1=W_2\right)$

So, $f_1=-f_2$

$\Rightarrow \frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{d}{f_1{f}_2}$

for achromatic comb

$\alpha =\frac{f_1+f_2}{2}$

$4\times 2=5+f_2$

$8-5=f_2$

$f_2=3cm$