#### Question

A convex lens of focal length 25 cm and a concave lens of focal length 10 cm are placed in close contact with one another.

(*a*) What is the power of this combination?

(*b*) What is the focal length of this combination?

(*c*) Is this combination converging or diverging?

#### Solution

Focal length of convex lens *f _{1} *= + 25 cm = + 0.25 m

Power of convex lens`p_1=1/(f_1)=1/0.25=4D`

Focal length of concave lens f_{2} = - 10 cm = - 0.10 m

Power of concave lens `p_2=1/(f_2)=1/-0.10=-10D`

(a) The power of the combination of lenses is the algebraic sum of the powers of the individual lenses.

∴ Power of combination P = P_{1} + P_{2}

⇒ P = 4 - 10 = - 6 D.

(b) Suppose, the focal length of the combination of the lenses is *f.*

The power of a lens and the focal length are related as:

`p=1/f`

`-6=1/f`

`f=1/-6=-0.167m -16.7 cm`

Therefore, the focal length of the combination of the lenses is - 16.7 cm.

(c) The focal length of the combination of the lenses is - 16.7 cm. Here, the negative sign shows that the combination of the two lenses acts like a concave lens. Therefore, this combination of lenses is diverging.