A person needs a lens of power $-4.5\ D$ for correction of her vision. $(a)$. What kind of defect in vision is she suffering from? $(b)$. What is the focal length of the corrective lens? $(c)$. What is the nature of the corrective lens?
$(a)$. She is suffering from myopia because the power of the lens is negative. In other words, it can be said nearsightedness, when a person can see objects clearly near to him/her but the objects placed far away seems to be blurry.
$(b)$. We know the relationship between the power of the lens and its focal length.
$\boxed{P=\frac{1}{f}}$
Here, $P\rightarrow$ power of the lens
$f\rightarrow$ focal length of the lens
Here given, power of the lens $P=-4.5\ D$
Therefore, focal length of the lens, $f=\frac{1}{P}$
$=\frac{1}{-4.5}\ m$
$=-0.22\ m$
$=-22\ cm$ [as $1\ m=100\ cm$]
$(c)$. As the focal length of the lens is negative, so the lens is a concave lens.