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. 0

Answer 1

Answer: (A)

Since, the person is not able to see distant objects beyond $10\, cm$ so, he should use concave lens in his spectacles.
Concave lens will form the image of object distant $30\, cm$, at $10\, cm$ it means
$u=-30\, cm , v=-10\, cm$
$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$
$=\frac{1}{-10}-\frac{1}{-30}=-\frac{2}{30}$
or $\frac{1}{f}=-\frac{1}{15}$
So, $f=-15\, cm$
Minus sign signifies that lens used in concave.