Question

Diameter of human eye lens is $2 \,mm$. What will be the minimum distance between two points to resolve them, which are situated at a distance of $50 \,m$ from eye? The wavelength of light is $5000\,\mathring{A} $.

• A. 2.32 m
• B. 4.28 mm
• C. 1.25 cm
• D. 12.48 cm

Answer 1

Answer: (C)

Angular limit of resolution of eye is the ratio of wavelength of light to diameter of eye lens.
Angular limit of resolution of eye
$=\frac{\text { Wavelength of light }}{\text { Diameter of eye lens }}$
ie, $ \theta=\frac{\lambda}{d}$...(i)
If $y$ is the minimum resolution between two objects at distance $D$ from eye, then
$\theta=\frac{y}{D}$ ..(ii)
From Eqs. (i) and (ii), we have
$\frac{y}{D}=\frac{\lambda}{d}$
or $ y=\frac{\lambda D}{d}$...(iii)
Given, $\lambda=5000 \,\mathring{A} =5 \times 10^{-7} m$,
$D=50 \,m$, $d=2 \,mm =2 \times 10^{-3} m$
Substituting in Eq. (iii), we get
$ y =\frac{5 \times 10^{-7} \times 50}{2 \times 10^{-3}} $
$=12.5 \times 10^{-3} m $
$=1.25 \,cm $