Question

A beam of parallel rays is brought to focus by a plano-convex lens. A thin biconcave lens of same focal length is joined to the first lens as shown in the figure. Which of the following statements is true?

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

Answer 1

The correct option is A The focus shifts to infinity.

Let $f_1$ and $f_2$ be the focal lengths of the plano-convex lens and bi-concave lens respectively.

We know that, if lenses are placed in contact, the focal length of the equivalent lens can be given as,

$\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}$

From the data given in the question, $|f_1|=|f_2|=f_0\left(\text{say}\right)$

Focal length of converging lens is taken as positive and that of diverging lens is taken as negative.

$\therefore \frac{1}{f}=\frac{1}{f_0}-\frac{1}{f_0}$

$\Rightarrow f=\infty$

Hence option (a) is the correct answer.

Why this question? Note:- If two or more lenses are in contact, the equivalent focal length is given by the formula $\frac{1}{f}=\sum _{i=1}^n\frac{1}{f_i}$