Question

In an experiment to obtain interference patterns on a screen, light of wavelength 600 nm was used to illuminate two slits separated by a distance of 0.034 mm. If the distance of the slits to the screen was 1.1 m, calculate the angle that the second dark fringe makes with the central axis.

a) 0.028∘
b) 0.056∘
c) 0.112∘
d) 0.224∘

Answer 1

To find the angle of the second dark fringe, use the formula d sin(theta) = (m + 1/2) lambda with m=1 for second dark fringe, leading to the answer of approximately 0.056°, which corresponds to option (b).

Step-by-step explanation:

To calculate the angle theta that the second dark fringe makes with the central axis in an interference pattern experiment, we use the formula for the position of the dark fringes in a double slit experiment: d sin(theta) = (m + 1/2) lambda, where d is the separation between the slits, m is the order of the dark fringe, and lambda is the wavelength of light. Since we're asked for the second dark fringe, m = 1. Therefore:

d sin(theta) = (1 + 1/2) * 600 nm

Convert the wavelength from nanometers to millimeters to match the slit separation units:

600 nm = 0.0006 mm

Now, calculate the angle theta:

0.034 mm * sin(theta) = 3/2 * 0.0006 mm

sin(theta) = (3/2 * 0.0006 mm) / 0.034 mm

sin(theta) = 0.00002647

theta = sin⁻¹(0.00002647)\

theta = 0.056° (approximately)

Option (b) 0.056⁰ is the correct answer. This approach relies on the principle of interference seen in double slit experiments.