Question

What is meant by power of a lens? Write its SI unit. A student uses a lens of focal length of 40 cm and another of -20 cm. Write the nature and power of the lens.

Answer 1

Hint: Define a lens. A lens will either converge or diverge the incoming light rays from each-other or from the principal axis. We can measure this amount of convergence or divergence of a lens. This gives the strength or power of a lens. Obtain the mathematical expression giving the total power of a lens system.

Complete step-by-step answer:
Power of a lens can be defined as the bending strength of a lens. The more the lens can bend the light rays passing through it, the more the power of the lens.
The power of a lens can be defined as the reciprocal of the focal length of the lens. Mathematically we can express this as,
$P=\dfrac{1}{f}$
Where, P is the power of the lens and f is the focal length of the lens in meters.
The unit of focal length is dioptres(D).
If we have two thin lens of power ${{P}_{1}}$ and ${{P}_{2}}$ close together, the total power of the lens system is given as,
$P={{P}_{1}}+{{P}_{2}}$
Now, we have two lenses with focal length ${{f}_{1}}=40cm=0.4m$ and ${{f}_{2}}=-20cm=-0.2m$
Total power of the lens system will be,
$\begin{align}
  & P={{P}_{1}}+{{P}_{2}} \\
 & P=\dfrac{1}{{{f}_{1}}}+\dfrac{1}{{{f}_{2}}} \\
 & P=\dfrac{1}{0.4}+\dfrac{1}{\left( -0.2 \right)} \\
 & P=\dfrac{1}{0.4}-\dfrac{1}{0.2} \\
 & P=2.5-5 \\
 & P=-2.5D \\
\end{align}$
So, the power of the lens is -2.5D.
Since the power is negative, the light will diverge from each other. So, we can say that the system of the lenses acts like a convex lens.

Note: A convex lens has a positive focal length. So, the power of a convex lens is positive. Again, the focal length of a concave lens is negative. So, the power of a concave lens is negative. So, we can say that if a lens diverges the light rays, it will have negative power and if a lens converges the light rays, it will have positive power.