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EEJ MAIN Physics QUESTION #7046
Question 1
Given a human pupil radius of $0.25 \text{ cm}$ and a viewing distance of $25 \text{ cm}$, what is the minimum distance between two objects that the eye can resolve at a wavelength of $500 \text{ nm}$?
  • $1 \ \mu\text{m}$
  • $30 \ \mu\text{m}$✔️
  • $100 \ \mu\text{m}$
  • $300 \ \mu\text{m}$
Correct Answer Explanation

The limit of resolution (angular) is $\Delta \theta = \frac{1.22 \lambda}{D}$, where $D$ is the diameter ($2 \times 0.25 = 0.5 \text{ cm} = 0.005 \text{ m}$).

Minimum separation $y = d \cdot \Delta \theta = \frac{1.22 \lambda d}{D}$

$y = \frac{1.22 \times 500 \times 10^{-9} \times 0.25}{0.005} \approx 30.5 \times 10^{-6} \text{ m} = 30.5 \ \mu\text{m}$.