#### Question

A convex lens of power 5 D and a concave lens of power 7.5 D are placed in contact with each other. What is the :

(*a*) power of this combination of lenses?

(*b*) focal length of this combination of lenses?

#### Solution

(a) Power of convex lens P_{1} = + 5 D

Power of concave lens P_{2} = - 7.5 D

The combined power is the algebraic sum of the individual powers of the lenses.

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

P = 5 D - 7.5 D = - 2.5 D

Therefore, the power of the combination of the lenses is - 2.5 D.

(b) The power and focal length are related as:

`p=1/f`

`-2.5=1/f`

∴ f=`-1/2.5=-0.4m=-40 cm`

Therefore, the focal length of the combination of the lenses is 40 cm. The negative sign shows that the combination of the two lenses causes it to behave like a concave lens.