Question

A beam of parallel rays is brought to focus by a planoconvex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is

• A. the focus shifts to infinity
• B. the focal point shifts towards the lens by a small distance
• C. the focal point shifts away from the lens by a small distance
• D. the focus remains undisturbed

Answer 1

Answer: (A)

The combined focal length of plano-convex lens
$\frac{1}{F}=\frac{1}{f_1}+\frac{1}{f_2}$
Hence, $f_1=\infty$ (for plane surface), $f_2=f$ (say)
$\therefore \frac{1}{F}=\frac{1}{\infty }+\frac{1}{f}$
$\Rightarrow F=f$
Now, when concave lens of same focal length is joined to first lens, then combined focal length
$\frac{1}{F^{\prime }}=\frac{1}{F_1}+\frac{1}{F_2}$
$=\frac{1}{f}-\frac{1}{f}\left(\because F_1=f,F_2=-f\right)$
$=0$
$F^{\prime }=\infty$
Thus, the image can be focussed on infinity $(\infty )$ or focus shifts to infinity.