A paper with two marks of separation d is held normal to the line of sight of an observer at distance 50 m. Diameter of the eye lens is 2 mm. What is the least value of d when marks can be seen as separate? Mean wavelength 5000 Å.
Options

Question

A paper with two marks of separation d is held normal to the line of sight of an observer at distance 50 m. Diameter of the eye lens is 2 mm. What is the least value of d when marks can be seen as separate? Mean wavelength 5000 Å.

Options

G1 Physics · Accepted Answer

Step 1: Rayleigh angular resolution approximately θ ≈ λ/D_aperture. Step 2: Required angular separation θ = d/L. Thus d = λL/D_aperture. Step 3: d = (5 × 10⁻⁷ × 50)/(2 × 10⁻³) = 12.5 × 10⁻³ m = 1.25 cm. Final answer: (C) 1.25 cm. (Using 1.22 Rayleigh prefactor would give about 1.53 cm.)