Question 15: Ray Optics

Question

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

Accepted Answer

For two thin lenses in contact, the total power P is the sum of their individual powers :
$$ \mathrm{P}=\mathrm{P}_1+\mathrm{P}_2 $$
The power of lens is given as $P=\frac{1}{f}$, where $f$ is the focal length of lens in meters.
$$ \frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2} $$
For a convex lens, the focal length is positive $\Rightarrow \mathrm{f}_1=+\left|\mathrm{f}_{	ext {convex }}ight|$.
For a concave lens, the focal length is negative $\Rightarrow f_2=-\left|f_{	ext {concave }}ight|$.
Substituting these into the formula of equivalent power:
$$ \frac{1}{F}=\frac{1}{\left|f_{	ext {convex }}ight|}-\frac{1}{\left|f_{	ext {concave }}ight|} $$
$$\Rightarrow $$ $$ \frac{1}{F}=\frac{\left|f_{	ext {concave }}ight|-\left|f_{	ext {convex }}ight|}{\left|f_{	ext {convex }}ight| \cdot\left|f_{	ext {concave }}ight|} $$
The combination behaves as a concave lens if the equivalent focal length F is negative ( $\mathrm{F}\left|\mathrm{f}_{	ext {concave }}ight| \end{gathered} $$
Conversely, it behaves as a convex lens if F is positive, which happens when
$$ \left|\mathrm{f}_{	ext {concave }}ight|>\left|\mathrm{f}_{	ext {convex }}ight| . $$
For thin lenses in contact, the formula $\frac{1}{\mathrm{~F}}=\frac{1}{\mathrm{f}_1}+\frac{1}{\mathrm{f}_2}$ is independent of the order of the lenses. Therefore, interchanging them does not change the focal length.
Therefore, the system behaves as a concave lens if $\left|\mathrm{f}_{	ext {convex }}ight|>\left|\mathrm{f}_{	ext {concave }}ight|$.
Thus, the correct option is (A).

Answer

behaves as concave lens if $\left|f_{	ext {convex }}ight|>\left|f_{	ext {concave }}ight|$

Answer

behaves as concave lens if $\left|f_{	ext {convex }}ight|<\left|f_{	ext {concave }}ight|$

Answer

behaves as convex lens if $\left|f_{	ext {convex }}ight|>\left|f_{	ext {concave }}ight|$

Answer

Focal length of the lens system will change if the positions of two lenses are interchanged

Ray Optics

A thin convex lens and a thin concave lens are kept in contact and are co-axial. Which of the following statements is correct for this combination of two lenses ?

Choose the correct answer: