A 450 nm laser shines light through a double slit of 0.2 mm separation. If a screen is placed 4 m behind the double slit, how wide are the bright fringes of the diffraction pattern?

• A. 9.0 mm
• B. 4.5 mm
• C. 2.2 mm
• D. 0.055 mm

Answer: (A)

Verified step by step guidance

1. Identify the formula for the fringe width in a double-slit experiment: \( w = \frac{\lambda L}{d} \), where \( w \) is the fringe width, \( \lambda \) is the wavelength of the light, \( L \) is the distance to the screen, and \( d \) is the separation between the slits.
2. Convert all measurements to consistent units. The wavelength \( \lambda = 450 \text{ nm} = 450 \times 10^{-9} \text{ m} \), the slit separation \( d = 0.2 \text{ mm} = 0.2 \times 10^{-3} \text{ m} \), and the distance to the screen \( L = 4 \text{ m} \).
3. Substitute the values into the formula: \( w = \frac{450 \times 10^{-9} \times 4}{0.2 \times 10^{-3}} \).
4. Simplify the expression by calculating the numerator and the denominator separately, then divide the results to find the fringe width \( w \).
5. Interpret the result to determine which of the given options (9.0 mm, 4.5 mm, 2.2 mm, 0.055 mm) matches the calculated fringe width.