Question

The width of a single slit if the first minimum is observed at an angle 2\(^\circ\) with a light of wavelength 6980 \AA\ is

• A. 0.2 mm
• B. \(2 \times 10^{-5}\) mm
• C. \(2 \times 10^5\) mm
• D. 2 mm

Hint:

For single slit diffraction minima: \(a\sin\theta = n\lambda\) (n = 1, 2, ...). For small angles \(\sin\theta \approx \theta\) (in radians).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Condition for first minimum in single slit diffraction: \(a\sin\theta = \lambda\).
Step 2: Detailed Explanation:
\[ a = \frac{\lambda}{\sin\theta} = \frac{6980 \times 10^{-10}}{\sin 2^\circ} = \frac{6980 \times 10^{-10}}{0.0349} \approx 2 \times 10^{-4} \text{ m} = 0.2 \text{ mm} \]
Step 3: Final Answer:
The slit width is 0.2 mm.