In a double-slit setup with slit separation d and distance to the screen L, the fringe spacing Δy between adjacent bright fringes is given by which expression?

In a double-slit setup with slit separation d and distance to the screen L, the fringe spacing Δy between adjacent bright fringes is given by which expression?

• A. Δy = λ L / d
• B. Δy = d L / λ
• C. Δy = λ d / L
• D. Δy = L / (λ d)

Answer: (A)

In double-slit interference, bright fringes occur when the extra path length from the two slits equals an integer multiple of the wavelength. The path difference is approximately d sin θ, where θ is the angle to a bright fringe. For small angles, sin θ ≈ tan θ ≈ y/L, so the position of the m-th bright fringe is y_m ≈ m λ L / d. The spacing between adjacent bright fringes is Δy = y_{m+1} − y_m ≈ λ L / d. This shows the fringe spacing grows with wavelength and with the screen distance, and shrinks as the slit separation increases. The other expressions mix the variables in ways that don’t match this behavior or violate dimensional consistency.

In double-slit interference, bright fringes occur when the extra path length from the two slits equals an integer multiple of the wavelength. The path difference is approximately d sin θ, where θ is the angle to a bright fringe. For small angles, sin θ ≈ tan θ ≈ y/L, so the position of the m-th bright fringe is y_m ≈ m λ L / d. The spacing between adjacent bright fringes is Δy = y_{m+1} − y_m ≈ λ L / d. This shows the fringe spacing grows with wavelength and with the screen distance, and shrinks as the slit separation increases. The other expressions mix the variables in ways that don’t match this behavior or violate dimensional consistency.