Question

Two thin convex lens of power +5 and +4 diopter are placed co-axially at distance 10cm .find the focal length of the combination

Answer 1

Total power=-15D +5D =-10D

Power of lens=P=1/F

F=1/p

1/-10

= -0.1m =-10cm

Answer 2

Given,

Power of two lenses are $P_{1}=+5D$ and $P_{2}=+4D$

We know that the The lens power is the inverse of the focal length in meters

therefore,

$Focal length in meters (f)=\frac{1}{Power(P)}$

Focal length of lens 1 = $f_{1}=\frac{1}{P_{1}}=\frac{1}{5}=0.2 m=20 cm$

Focal length of lens 2 $f_{2}=\frac{1}{P_{2}}=\frac{1}{4}=0.25 m=25 cm$

The effective focal length (f) of a system of two lenses, separated by a distance d, is given by:

$f=\frac{f_{1}\times{f}_{2}}{f_{1}+f_{2}-d}\\\\\Rightarrow{f}=\frac{20\times25}{20+25+10}\\\\\Rightarrow{f}=\frac{500}{35}\\\\\Rightarrow{f}=14.28$ cm

Hence, the effective focal length of the given system of lenses is +14.28 cm.