Question

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

Answer 1

Hint
In this problem the power of the lens is given and we have to determine the focal length of the lens. By using the relation between the power of lens and the focal length, then the focal length of the lens can be determined.
Power of lens,
$p = \dfrac{1}{f}$
Where, $p$ is the power of the lens and $f$ is the focal length of the lens.

Complete step by step solution
Given data: The power of lens, $p = + 1.5\,D$
The relation between the power of lens is equal to the reciprocal of the focal length,
$p = \dfrac{1}{f}\,...................\left( 1 \right)$
We need to find the focal length, then the above equation can be written as,
$f = \dfrac{1}{p}$
Now substitute the power of lens in the above equation, then
$f = \dfrac{1}{{1.5}}$
For easy simplification, multiply and divide by $10$ in RHS, then,
$f = \dfrac{1}{{1.5}} \times \dfrac{{10}}{{10}}$
 Now the above equation is written as,
$f = \dfrac{{10}}{{15}}$
On dividing, then the above equation is written as,
$f = 0.67\,m$
Thus, the focal length of the lens for the given power is $0.67\,m$
Thus, for the given power of lens, the focal length value is positive then the lens is converging in nature.

Note
While calculating the focal length, in one step we have to multiply and divide by $10$, so we have to give more concentration in this step. If the focal length of the lens is positive, then the lens is converging in nature. If the focal length of the lens is negative, then the lens is diverging in nature.