Question

A person suffering from the eye-defect myopia (short-sightedness) can see clearly only up to a distance of 2 metres. What is the nature and power of lens required to rectify this defect?

Answer 1

A person suffering from myopia can correct the defect by wearing spectacles with concave lenses. In order to find the power of the concave lens required, we have to first calculate its focal length.
Given that the far point of the myopic person is 2 m from the eye (the person can see an object kept at infinity if the image of the object is formed at the far point of 2 m from the eye).
u = ∞ (distance of the object)
v = -2 m (far point in front of the lens)
f = ? (focal length)
The focal length can be calculated using the lens formula $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$.
Substituting the values in the formula, we get $\frac{1}{-2}-\frac{1}{\infty }=\frac{1}{f}$.
∴ f = -2 m
Now that we know the focal length of the concave lens, the power can be calculated.
Power $P=\frac{1}{f(inmetres)}$
$P=\frac{1}{-2}=-0.5\text{dioptres}$
Therefore, the power of the concave lens required to rectify the defect is -0.5 dioptres.