Question

White light is passed through the double slit and interference pattern is observed on a screen 2.5 m away. The separation between the slits is 0.5 mm. The first violet and red fringes are formed at distances of 2 mm and 3.5 mm away from the central white fringe respectively. Calculate wavelengths of red and violet light.

A. 800 nm and 400 nm
B. 350 nm and 200 nm
C. 750 nm and 350 nm
D. 700 nm and 400 nm

Answer 1

To calculate the wavelengths of red and violet light in an interference pattern, use the formula y = (m\(\lambda)L)/d. The wavelengths are found to be 400 nm for violet and 700 nm for red light, using the given distances for the first fringes of each color.

Step-by-step explanation:

The wavelengths of red and violet light in the observed interference pattern can be calculated using the formula for the position of bright fringes in a double-slit experiment, which is:

y = (m\(\lambda)L)/d

Where:

• y is the distance from the central maximum to the fringe.
• m is the order of the fringe (for first-order maximum, m = 1).
• \(\lambda) is the wavelength of the light.
• L is the distance between the slits and the screen.
• d is the separation between the slits.

To find the wavelengths of the violet and red light, we solve the equation for \(\lambda):

\(\lambda = (y*d)/(m*L)

For the first violet fringe (m = 1, y = 2 mm, d = 0.5 mm, L = 2.5 m), the wavelength \(\lambda_violet) is:

\(\lambda_violet = (2*10^{-3} m * 0.5*10^{-3} m) / (1 * 2.5 m) = 400 nm

And for the first red fringe (m = 1, y = 3.5 mm, d = 0.5 mm, L = 2.5 m), the wavelength \(\lambda_red) is:

\(\lambda_red = (3.5*10^{-3} m * 0.5*10^{-3} m) / (1 * 2.5 m) = 700 nm