26. A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate ? The mean wavelength of visible light may be taken as 5000Å ?

26. A paper, with two marks having separation d, is held normal to the line of sight of an observer at a distance of 50 m. The diameter of the eye-lens of the observer is 2 mm. Which of the following is the least value of d, so that the marks can be seen as separate ? The mean wavelength of visible light may be taken as 5000Å ?

(a) 1.25 m

(b) 12.5 cm

(c) 1.25 cm

(d) 2.5 mm

Answer :  (c) 1.25 cm

\( d\theta_{\min} = \frac{\lambda}{a} \)

\( = \frac{5000 \, \text{Å}}{2 \times 10^{-3}} \)

\( d = d\theta_{\min} \cdot 50 \)

\( = \frac{5000 \, \text{Å}}{2 \times 10^{-3}} \times 50 \)

\( = \frac{25}{2} \times 10^{-3} \)

\( = 12.5 \times 10^{-3} \)

\( = 1.25 \, \text{cm} \)