Question

A short-sighted person can see objects most distinctly at a distance of $16cm$. If he wears spectacles at a distance of $1cm$ from the eye, then their focal length to see at a distance of $26cm$ distinctly is

• A. $25cm,convex$
• B. $25cm,concave$
• C. $37.5cm,convex$
• D. $37.5cm,concave$

Answer 1

Answer: (D)

$37.5cm,concave$

The farthest that the person can see is 16 cm. It means that rays coming from an object, which is 16 cm away from the eye, can be focused properly. When the person wears spectacles, the eyes don't see the objects directly, instead they see only the image of the objects formed by the lenses of the spectacles. So, in order to see some thing 26 cm away we should make sure that the image of object formed by spectacles should be 16 cm away so that eye could focus the rays coming from the image.

• Object is 26 cm away from eye or 25 cm away from the lens of the spectacles ($u=-25cm$)
• Image is 16 cm from the eye or 15 cm away from the lens of the spectacles ($v=-15cm$)

(Taking the left side to the lens of spectacle to be positive)

Lens formula: $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

Substituting $u$ and $v$ in the lens equation:

$\frac{1}{-15}-\frac{1}{-25}=\frac{1}{f}$

$\frac{-5}{75}+\frac{3}{75}=\frac{1}{f}$

$\frac{-2}{75}=\frac{1}{f}$

$\Rightarrow f=-75/2=-37.5cm$

Focal length is negative & rays are coming from right to left. That means lens is concave.