Question

A converging and a diverging lens of equal focal lengths are placed co axially in contact that the power and the focal length of the combination

Answer 1

The correct answers to the question will be $\ \infty$ and 0.

CALCULATION:

We have been given that the focal length of both lens are equal .

Let the focal length of the converging and diverging lens are denoted as .$f_{1}\ and\ f_{2}\ respectively$

The focal length of a convex or converging lens is taken as positive.

Hence, $f_{1}\ =\ +f$

The focal length of a concave or diverging lens is taken as negative.

Hence, $f_{2}=\ -f$

The two lens are placed co-axially in contact to each other.

The combined focal length $F=\ \frac{f_{1} f_{2}} {f_{1}+f_{2}}$

                                                    $=\ \frac{f\times (-f)}{f+(-f)}$

                                                    $=\ \infty$

The power of a lens is the reciprocal of focal length

Hence, the combined power of the lens is calculated as -

                                    combined power P = $\frac{1}{F}$

                                                                     = $\frac{1}{\infty}$

                                                                    = 0                   [ans]