Question

If the powers of the lenses L1 and L2 are in the ratio of 4:1, what would be the
ratio of the focal length of L1 and L2?
a) 4:1
b) 1:4
c) 2:1
d) 1:1

Answer 1

Answer :

option B is correct 1 : 4

The ratio of the powers of the lenses L₁ and L₂ = 4 : 1

We have to find the ratio of their focal lengths.

Principle Focus (F) : It is the point of intersection of all reflected rays for which the incident rays strike the mirror (with small aperture) parallel to the principal axis. In convex lens it is real and in the concave lens it is virtual.

The distance from pole to focus is called focal length.

Ratio of powers = 4 : 1

Power of L₁ = 4x

Power of L₂ = 1x

We know that power is the reciprocal of focal length.

∴ Focal length of L₁ = 1/4x

∴ Focal length of L₂ = 1/x

Ratio of focal lengths ;

➝ f₁ : f₂ = 1 : 4

Answer 2

Given:

Ratio of power of lens is 4 : 1.

To find:

Ratio of focal length ?

Calculation:

$P_{L1} : P_{L2} = 4 : 1$

$\implies \: \dfrac{P_{L1}}{P_{L2}} = 4$

$\implies \: \dfrac{ \dfrac{1}{f_{L1}}}{ \dfrac{1}{f_{L2}}} = 4$

$\implies \: \dfrac{ f_{L2}}{f_{L1} }= 4$

$\implies \: \dfrac{ f_{L1}}{f_{L2} }= \dfrac{1}{4}$

$\implies \: f_{L1} : f_{L2} = 1 : 4$

So, ratio of focal length is 1 : 4.