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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?
Given:
A doctor has prescribed a corrective lens of power +1.5 D.
To do: To find the focal length of the lens and to determine the type of lens whether it is diverging or converging.
Solution:
Power of the lens:
The power of a lens implies the ability to bend a light passing through it.
The unit of power of a lens is Diopter$(D)$
The formula for the power of lens:
$\boxed{P=\frac {1}{f}}$
Here,
$P\rightarrow$ Power of the lens
$f\rightarrow$ focal length of the lens
It is given that power of the lens, $P$ = $+1.5\ D$
Substituting the given values we get-
$+1.5=\frac {1}{f}$
Or $f=+\frac {1}{1.5}$
Or $f=+\frac {10}{15}$
Or $f=+0.666\ m=+66.6\ cm$
Therefore,
The focal length of the lens:
The focal length of the lens $f$ is 66.6 cm.
Nature of the lens:
The negative sign $(+)$ implies that the lens is converging in nature. Hence, it is a convex lens.
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