Question

A person who can see things most clearly at a distance of $10 \,cm$ requires spectacles to enable to see clearly things at a distance of $30\, cm$. What should be the focal length of the spectacles?

• A. 15 cm (concave)
• B. 15 cm (convex)
• C. 10 cm
• D. Zero

Answer 1

Answer: (A)

The defect of short-sightedness is removed by using a lens which diverges the rays from object.
The person can see near object $(10\, cm )$ but cannot see the distant objects distinctly.
In order to remove this defect a concave lens of suitable focal length is used which diverges the rays from a distant object reaching the eye such that they appear to be coming from the eye's own far point $P$.
From lens formula

$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}=-\frac{1}{10}-\left(-\frac{1}{30}\right)=-\frac{2}{30}$
$\Rightarrow \frac{1}{f}=-\frac{1}{15} $
$\Rightarrow f=-15\, cm $