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 mathringA .

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 mathringA . (A) 2.32 m (B) 4.28 mm (C) 1.25 cm (D) 12.48 cm

Tardigrade Admin · Accepted Answer

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{Wavelength of light}{Diameter of eye lens}

ie,

θ = \frac{λ}{d}

...(i)
If

y

is the minimum resolution between two objects at distance

D

from eye, then

θ = \frac{y}{D}

..(ii)
From Eqs. (i) and (ii), we have

\frac{y}{D} = \frac{λ}{d}

or

y = \frac{λ D}{d}

...(iii)
Given,

λ = 5000 \overset{˚}{A} = 5 \times 1 0^{- 7} m

,

D = 50 m

,

d = 2 mm = 2 \times 1 0^{- 3} m

Substituting in Eq. (iii), we get

y = \frac{5 \times 1 0 ^{- 7} \times 50}{2 \times 1 0 ^{- 3}}

= 12.5 \times 1 0^{- 3} m

= 1.25 c m

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

2.32 m

4.28 mm

1.25 cm

12.48 cm

Q. 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 $5000 \overset{˚}{A}$ .