Question

A nearsighted person cannot see objects clearly beyond $25.0cm$ (her far point). If she has no astigmatism and contact lenses are prescribed for her, -'what power and type of lens are required to correct her vision ?

Answer 1

Nearsighted person has myopia.

Given far point =25.0 cm, to correct vision we need to shift far point at infinity.

See diagram, using lens formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ in this question $u=-25$ $cm$ and $v=\infty$

$\frac{1}{f}=\frac{1}{-\infty }-\frac{1}{-25}$

$\frac{1}{f}=-\frac{1}{25}⟹f=-25cm=-0.25m$

power of a lens $P=\frac{1}{f}$ where f is in meter and $P$ is in Diopter.

so $P=\frac{1}{-0.25}=-4D$

power of lens $4$ $D$, and $-$sign signifies lens is diverging i.e concave lens