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) -2.5D

b) -40cm

as concave lens has power of lens in negative sign it is -7.5D and convex lens +5D

p =p1 +p2

p=-7.5D+5D =-2.5D

B) power of lens =1/focal length

f=1/power of lens

f=1/-2.5D*100f=-40cm or -0.4m

Answer 2

Power of this combinations of lenses = -2.5

Focal length of this combinations of lenses = -40 cm

Explanation:

Given,

Convex lens power P 1 = 5 D

Concave lens power P 2 = - 7.5 D

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

so,

Combinations Power,  $P=P 1+P 2$

$P=5 D-7.5 D$

$P=-2.5 D$

(a) Therefore, the power of combinations is $-2.5 \mathrm{D}.$

(b) Focal length can be calculated based on below formula,

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

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

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

$\Rightarrow f=-0.4 m=c m$

$=-40 \mathrm{cm}$

So, the focal length is - 40cm.