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?

Answer 1

(a) Power of convex lens P₁ = + 5 D
     Power of concave lens P₂ = - 7.5 D
The combined power is the algebraic sum of the individual powers of the lenses.
∴ Power of the combination P = P₁ + P₂
                                            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: 

${\displaystyle p=\frac{1}{f}}$ 

${\displaystyle -2.5=\frac{1}{f}}$ 

∴ f=${\displaystyle -\frac{1}{2.5}=-0.4m=-40cm}$ 

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.