Question

(a) What is short-sightedness? State the two causes of short-sightedness (or myopia). With the help of ray diagrams, show:
(i) the eye-defect short-sightedness.
(ii) correction of short-sightedness by using a lens.
(b) A person having short-sight cannot see objects clearly beyond a distance of 1.5 m. What would be the nature and power of the corrective lens to restore proper vision?

Answer 1

(a) Short-sightedness, or near-sightedness, is an eye defect because of which a person cannot see distant objects clearly but has normal near vision. Short-sightedness occurs because of the high converging power of the eye lens (images are formed in front of the retina) and because the eyeball is too long (images are formed in front of the retina).

(i) and (ii) The following diagram illustrates short-sightedness and how concave lenses can correct the defect by diverging the light rays entering the eye to form clear images of distant objects on the retina.



(b) A person suffering from short-sightedness can correct the defect by wearing spectacles fitted with concave lens. In order to find the power of the concave lens, we have to first calculate its focal length.
Given, the far point of the short-sighted person is 1.5 m from the eye (the person can see the object kept at infinity if the image of the object is formed at the person's own far point of 1.5 m from the eye).

$u=\infty$ (the distance of the object)
$v=-1.5m$ (far point of the defective eye in front of the lens)
f = ? (focal length)
The focal length can be calculated using the lens formula $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$.
Substituting the values in the formula, we get
$$\begin{gathered} \frac{1}{-1.5}-\frac{1}{\infty }=\frac{1}{f} \\ f=-1.5m, \\ \mathrm{Since},\frac{1}{\infty }=0 \end{gathered}$$

Now, that we know the focal length of the concave lens, its power can be calculated.
Power $P=\frac{1}{f}(finmetres)$
∴ $\mathrm{P}=\frac{-1}{1.5}=-0.667\mathrm{Dioptres}\approx -0.67\mathrm{Dioptres}$
Hence, the power of the concave lens required to rectify the defect is -0.67 D.