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EEJ MAIN Physics QUESTION #7024
Question 1
The central maximum in a single slit diffraction has an angular width of $60^\circ$ for a slit $1 \ \mu\text{m}$ wide. If two such slits are used in a YDSE setup with a screen $50 \text{ cm}$ away and a fringe width of $1 \text{ cm}$ is observed, what is the separation between the slits?
  • $75 \ \mu\text{m}$
  • $100 \ \mu\text{m}$
  • $25 \ \mu\text{m}$✔️
  • $50 \ \mu\text{m}$
Correct Answer Explanation

Angular width $2\theta = \frac{2\lambda}{a} = 60^\circ = \frac{\pi}{3} \text{ rad}$.

$\frac{\lambda}{a} = \frac{\pi}{6} \implies \lambda = \frac{\pi}{6} \times 1 \ \mu\text{m}$.

Fringe width $\beta = \frac{\lambda D}{d} = 1 \text{ cm} = 10^{-2} \text{ m}$.

$d = \frac{\lambda D}{\beta} = \frac{(\pi/6 \times 10^{-6}) \times 0.5}{0.01} \approx 26.1 \ \mu\text{m}$. The closest option is $25 \ \mu\text{m}$.