Question

A person suffering from short-sightedness can see up to 80 meters. Calculate the nature and focal length of the lens to correct his vision so that he may see the objects at infinite distance.

Hint:

For short-sightedness, use a concave lens to diverge the light rays and bring the focus to the far point.

Answer 1

The far point of the person is \( 80 \, \text{m} \), and the person needs a lens that can focus at infinity.
For short-sightedness, a diverging lens (concave lens) is required. The formula for the focal length of a lens is: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] where \( v = \infty \) and \( u = -80 \, \text{m} \) (since the far point is 80 meters).
Substituting the values: \[ \frac{1}{f} = \frac{1}{\infty} - \frac{1}{-80} = \frac{1}{80} \] Thus, the focal length \( f = -80 \, \text{m} \). This means a concave lens of focal length \( 80 \, \text{m} \) is needed.