Question

A convex lens of focal length 20 cm is placed in contact with a concave lens of focal length 10 cm.calculate (1) power of each lens,(2) power of combination

Answer 1

focal of convex lens(f)=+20cm=20/100=+.20 m
P=1/f=1/.20=100/20=+5D

focal length of concave lens(f)=-10cm=-10/100=-.1 m
P=1/-.1=-10D

power of combination=5-10=-5D

Answer 2

The answers to the question are 5D, -10D and -5D

CALCULATION:

The focal length of convex lens is given as $f_{1}$ = 20 cm

                                                                          = 0.2 m

The focal length of a convex lens is always positive. So, the focal of convex lens will be + 0.2 m.

The focal length of the concave lens $f_{2}$ = 10 cm

                                                                     = 0.1 m

The focal length of a concave lens is always negative.

Hence, $f_{2}$ = - 0.1 m.

The power of a lens is defined as the reciprocal of focal length.

Mathematically power $p\ =\ \frac{1}{f}$

The power of a convex lens is calculated as -

                                          $power\ p_{1}\ =\ \frac{1}{f_{1}}$

                                                 $=\ \frac{1}{0.2}\ D$

                                                 $=\ 5\ D$

The power of the concave lens is calculated as -

                        $power\ p_{2}\ =\ \frac{1}{f_{2}}$

                                $=\ \frac{1}{- 0.1}\ D$

                                $=\ - 10\ D$

The two lens are placed in contact with each other.

Hence, the power of combination $p\ =\ p_{1} +p_{2}$

                                                                $=\ 5 D+(-10 D)$

                                                                $=\ -5 D$                [ANS]

Here, D stands for dioptre which is the unit of power.