Question

A doctor has prescribed a corrective lens of power $+1.5D$. Find the focal length of the lens. Is the prescribed lens diverging or converging?

Answer 1

Hint: A lens is an optical instrument which can converge or diverge the light falling on it. Since the power of the lens is given, we can calculate the focal length. Using the focal length we can identify if the lens is converging or diverging.

Formula used: $P=\dfrac{1}{f}$


Complete step-by-step answer:
Focal length of an optical system like a mirror, lens or any other system is the ability of the system to converge or diverge the light falling on it. If the focal length of the system is positive, then the system converges the light. If the focal length of the system is negative, then the system diverges the light. The focal length has SI unit meter.
Similarly, the optical power is the degree to which an optical system can converge or diverge the light falling on it. It is the reciprocal of the focal length of the system. It is measured in terms of dioptre $D$.
Given that the power $P=+1.5D$
We know that $P=\dfrac{1}{f}$ where $f$ is the focal length.
Then $f=\dfrac{1}{P}$
$f=\dfrac{1}{1.5}=0.66m$
Hence the focal length of the lens is $+0.66m$
Since the focal length is positive the lens is a converging lens.

Note:Power and focal length are interrelated, if one is given the other can be found easily. Also, if the focal length of the system is positive, then the system converges the light. If the focal length of the system is negative, then the system diverges the light.