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

Power of the combinations, P = -2.5

Focal length of the combinations f = -40 cm                                      

Explanation:

Given ,

Power of convex lens P 1 = 5 D

Power of concave lens P 2 = - 7.5 D

The combined power is the combinations of algebric sum of lenses,

so,

Power of the combinations, P = P 1 + P 2

                                               P = 5 D -7.5 D

P = - 2.5 D

(a)- therefore ,the power of combinations is - 2.5 D

(b)- Focal length of the combinations ,

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

⇒ f = $\frac{1}{p}$

⇒ f = $\frac{1}{-2.5}$

⇒ f = - 0.4 m  =$0.4\times 100$ cm

      = -40 cm

Answer 2

Focal Length of Both is - 40 cm

Explanation:

• Convex lens has Power $P_1$ = + 5 D

• Concave lens has Power $P_2$ = - 7.5 D

(a) Power of combination:

P = $P_1 + P_2$ = + 5 D + (- 7.5 D) = - 2.5 D

So, Combination of power = - 2.5 D

(b) Relation between Power and Focal Length is

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

or  

f = $\frac {1}{p}$  

= $\frac {1}{-2.5}$

= 0.4 m  

= - 40 cm

So, Focal length is - 40 cm.

The negative sign means the two lenses work together as a concave lens