Question

How is the power of a combination of lenses described? The powers of the lenses are $P_1,P_2,P_3$ and $P_4$.

Answer 1

Step 1: Given data,

The powers of the lenses are $P_1,P_2,P_3$, and $P_4$.

Step 2: Describe the power of a combination of lenses,

1. Power of lens is defined as the inverse of its focal length, that is, $Powerofalens=\frac{1}{focallengthofthelens}$
2. The net power of the combination of lenses is equal to the algebraic sum of powers of all lenses in the combination, that is, $P=P_1+P_2+P_3+P_4$.
3. As the power of the lens and the focal length are inversely related to each other, the relation $P=P_1+P_2+P_3+P_4$ can be expressed as $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\frac{1}{f_4}$, where, $f$ is the focal length of the combination of lenses and $f_1,f_2,f_3$ and $f_4$ are the focal lengths of the four lenses in combination.

Thus, the power of a combination of lenses is described as $P=P_1+P_2+P_3+P_4$ or $\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}+\frac{1}{f_3}+\frac{1}{f_4}$.