Question

Two luminous point sources separated by a certain distance are at 10 km from an observer. If the aperture of his eye is $2.5\times10^{-3}$ m and the wavelength of light used is 500 nm, the distance of separation between the point sources just seen to be resolved is

• A. 12.2 m
• B. 24.2 m
• C. 2.44 m
• D. 1.22 m

Hint:

Resolution limit depends on wavelength and aperture size; larger apertures provide better resolution.

Answer 1

The Correct Option is C

Step 1: Rayleigh's Criterion
The angular resolution is given by $\theta = \frac{1.22\lambda}{d_e}$. Substituting the values: $\theta = \frac{1.22 \times 500 \times 10^{-9}}{2.5 \times 10^{-3}} = 2.44 \times 10^{-4}$ rad.
Step 2: Linear Separation
The relationship between angular separation ($\theta$), distance ($D$), and linear separation ($a$) is $\theta = \frac{a}{D}$.
Step 3: Calculation
$a = D \times \theta = 10 \times 10^3 \times 2.44 \times 10^{-4} = 2.44$ m.
Final Answer: (c)