$A$ person cannot see objects distinctly when placed beyond $2\, m$.
$(a)$ Identify the eye defect.
$(b)$ Give two reasons for this defect.
$(c)$ Calculate the power and nature of the lens he should be using to see the distant objects clearly.
$(d)$ Draw the ray diagrams for the defective and the corrected eye.

(N/A) The eye defect is Myopia (nearsightedness).
$(b)$ The two reasons for this defect are:
$(i)$ Excessive curvature of the eye lens.
$(ii)$ Elongation of the eyeball.
$(c)$ To see distant objects clearly,the person needs a lens that forms a virtual image of an object at infinity at his far point $(2\, m)$.
Given: Object distance $u = \infty$,Image distance $v = -2\, m$.
Using the lens formula: $\frac{1}{f} = \frac{1}{v} - \frac{1}{u} = \frac{1}{-2} - \frac{1}{\infty} = -0.5\, m^{-1}$.
Power $P = \frac{1}{f(m)} = -0.5\, D$.
The negative sign indicates that the lens is a concave lens (diverging lens).
$(d)$ The ray diagrams are as shown in the provided image.