Question

Consider the compound optical system shown in the diagram, where two thin lenses of focal lengths 8.5 cm (left lens) and 5.5 cm (right lens) are separated by a distance 36 cm.

Answer 1

As per the given question,

focal length of the lenses are $(f_1)=8.5cm$

$f_2=5.5cm$

Distance between the lenses are $(d)=36cm$

Hence focal length of the lens will be $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}-\frac{36}{f_1f_2}$

Now, substituting the values,

$\frac{1}{f}=\frac{1}{8.5}+\frac{1}{5.5}$ $-\frac{36}{8.5\times 5.5}$

$\Rightarrow \frac{1}{f}=\frac{56}{187}-\frac{144}{187}$

$\Rightarrow \frac{1}{f}= \frac{-88}{187}cm$

$\Rightarrow f= \frac{-187}{88}cm$