If the power of lenses L1 and L2 in a ratio 4:1, what would be the ratio of focal length of L1 and L2?

A
$4 : 1$
B
$1 : 4$
C
$2 : 1$
D
$1 : 1$

Solution:

The ratio of focal length of

L_{1}

and

L_{2}

1 : 4

.
Given,
Ratio of the power of lenses

L_{1}

and

L_{2}

P_{1} : P_{2} = 4 : 1

It is known that “Power of a lens is the ability of a lens to converge or diverge light rays. It can be defined as the reciprocal of its focal length in meters.” Mathematically,

P = \frac{1}{f}

Where

P

is the power and

f

is the focal length in meters.
The given data can be written as

\Rightarrow \frac{P_{1}}{P_{2}} = \frac{4}{1}

Using the formula of power, we can write

\Rightarrow \frac{\frac{1}{f_{1}}}{\frac{1}{f_{2}}} = \frac{4}{1}

Where

f_{1}

is the focal length of lens

L_{1}

and

f_{2}

is the focal length of lens

L_{2}

.
On simplifying, we get

\Rightarrow \frac{f_{2}}{f_{1}} = \frac{4}{1}

Hence, the ratio of focal length of

L_{1}

and

L_{2}

1 : 4

If the power of lenses $L_{1}$ and $L_{2}$ in a ratio $4 : 1$ , what would be the ratio of focal length of $L_{1}$ and $L_{2}$ ?

Solution:

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