Question

White light falls on two narrow slits separated by 0.40 mm. The interference pattern is observed on a screen 3.0 m away. What is the separation between the first maxima for red light (λ=700nm) and violet light (λ=400nm)?

A. 1.8 mm
B. 2.0 mm
C. 2.5 mm
D. 3.6 mm

Answer 1

Using the double-slit interference formula, we found the separation between the first diffraction maxima for red and violet light to be approximately 2.25mm. Due to rounding, the closest possible answer choice is 2.5 mm., which is option (C).

Step-by-step explanation:

The question is asking for the separation between the first diffraction maxima for two different wavelengths of light, red (700nm) and violet (400nm), given that the setup uses a double slit with a separation of 0.40mm and the screen where the pattern is observed is 3.0m away.

To find the separation between the maxima, we can apply the double-slit interference formula:

1. Calculate the angle for the first maximum for each wavelength using the formula
   θ = λ/d, where λ is the wavelength and d is the slit separation.
2. Determine the position of the first maximum on the screen using x = L tan(θ), where L is the distance to the screen.
3. Find the difference between the two positions to determine the separation.

For red light (700nm):

1. θ_red = 700nm / 0.40mm = 1.75e-3 radians
2. x_red = 3.0m * tan(1.75e-3) ≈ 5.25mm

For violet light (400nm):

1. θ_violet = 400nm / 0.40mm = 1.00e-3 radians
2. x_violet = 3.0m * tan(1.00e-3) ≈ 3.00mm

The separation between the first maxima for red and violet light is therefore: x_red - x_violet = 5.25mm - 3.00mm = 2.25mm. The closest answer is option (C).