Question

(a) Draw a diagram to show the formation of image of a distant object by a myopic eye. How can such an eye defect by remedied?
(b) State two reasons due to which this eye defect may be caused.
​(c) A person with a myopic eye cannot see objects beyond a distance of 1.5 m. What would be the power of the corrective lens used to restore proper vision?

Answer 1

(a) A diagram to show the formation of an image of a distant object by a myopic eye is shown below:



The defect of a myopic eye can be corrected by using a concave lens. A concave lens helps in diverging the rays to form an image on the retina of the eye.

(b) Causes of myopia: (i) Elongation of the eyeball (ii) Decrease in the focal length of the eye lens.

(c) As it is a case of myopia one has to use a concave lens.
The far point is 1.5 m, it means that the image should be formed at 150 cm or before on the same side as the object. The distance of the object is taken as infinite, as the problem is nearsightedness.

Now, u = ∞, v = –150 cm and f = ?

Using the lens formula, $\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$

$$\begin{gathered} \Rightarrow \frac{1}{-150}-\frac{1}{\infty }=\frac{1}{f} \\ \Rightarrow \frac{1}{f}=\frac{1}{-150} \\ \Rightarrow f=-150\mathrm{cm} \end{gathered}$$

The maximum focal length to be used = $-150\mathrm{cm}$

Hence, the power of the lens required = $P=\frac{1}{f(\mathrm{in}\mathrm{meter})}=\frac{1}{1.5\mathrm{m}}=0.67\mathrm{D}$

Therefore, a concave lens with power 0.67 D or more is required for the correction in vision.