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\,??.

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

Answer 1

The Correct Option is 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, $\lambda=5000 \,??5 \times 10^{-7} m$, $D=50 \,m$, $d=2 \,mm =2 \times 10^{-3} m$ Substituting in E (iii), we get $ y =\frac{5 \times 10^{-7} \times 50}{2 \times 10^{-3}} $ $=12.5 \times 10^{-3} m $ $=1.25 \,cm $