Question

A light wave of wavelength 600 nm passes through a double-slit apparatus with a slit separation of 0.2 mm. What is the angular separation (in degrees) of the first-order bright fringe?

• A. 0.344°
• B. 0.172°
• C. 0.516°
• D. 0.688°

Hint:

Always convert units to SI (meters) for optics problems and use the small-angle approximation (\( \sin \theta \approx \theta \)) for simplicity.

Answer 1

The Correct Option is B

To find the angular separation of the first-order bright fringe in a double-slit experiment, we proceed as follows:

1. Use the formula for the angular position of the \( m \)-th bright fringe: \[ \sin \theta = \frac{m \lambda}{d}. \]
2. For the first-order fringe, set \( m = 1 \).
3. Given: wavelength \( \lambda = 600 \, \text{nm} \), slit separation \( d = 0.2 \, \text{mm} \).
4. Convert units to meters for consistency: \[ \lambda = 600 \, \text{nm} = 600 \times 10^{-9} \, \text{m} = 6 \times 10^{-7} \, \text{m}, \] \[ d = 0.2 \, \text{mm} = 0.2 \times 10^{-3} \, \text{m} = 2 \times 10^{-4} \, \text{m}. \]
5. Calculate \( \sin \theta \): \[ \sin \theta = \frac{1 \times 6 \times 10^{-7}}{2 \times 10^{-4}} = 3 \times 10^{-3}. \]
6. For small angles, use the approximation \( \sin \theta \approx \theta \) (in radians), so: \[ \theta \approx 3 \times 10^{-3} \, \text{radians}. \]
7. Convert radians to degrees: \[ \theta_{\text{degrees}} = 3 \times 10^{-3} \times \frac{180}{\pi} \approx 3 \times 10^{-3} \times 57.296 \approx 0.1719^\circ. \]
8. Compare with options: 0.1719° is rounded to 0.172°.

Thus, the correct answer is: \[ \boxed{0.172^\circ} \]