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Question: Two point white dots are I mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm....

Two point white dots are I mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? (Take wavelength of light= 500nm).

A

5 m

B

1 m

C

6 m

D

3 m

Answer

5 m

Explanation

Solution

: Resolution of pinhole camera=1.22λd= \frac{1.22\lambda}{d}

Here d is the diameter of the pupil.

Also, Resolution =SeparationofobjectsDistan⁡ceofobject\frac{Separationofobjects}{Dis\tan ceofobject}

1.22λd=1mmR\frac{1.22\lambda}{d} = \frac{1mm}{R}

⇒1.22×500×10−93×10−3=1×10−3R\Rightarrow \frac{1.22 \times 500 \times 10^{- 9}}{3 \times 10^{- 3}} = \frac{1 \times 10^{- 3}}{R}

⇒R=5m\Rightarrow R = 5m