Laser light sent through a double slit produces an interference pattern on a screen 3.00 m from the slits.If the eighth-order maximum occurs at an angle of 63.4°,at what angle does the third-order maximum occur?
A)No third-order maximum occurs.
B)0.34°
C)19.6°
D)23.8°
E)Not enough information is given.

Question

Quizplus · Accepted Answer

For double-slit interference, the path difference between two waves from the slits to a point on the screen determines the interference pattern. At the location of the maximum, the path difference between the waves from the two slits is equal to a whole number of wavelengths (n λ), where n is an integer. The path difference for the eighth-order maximum would be 8λ.

For small angles, the path difference can be approximated as d sinθ, where d is the distance between the two slits and θ is the angle measured from the center of the interference pattern. So, we can write:

8λ = d sin(63.4°)

We are asked to find the angle θ for the third-order maximum, which would correspond to a path difference of 3λ. Using the same formula, we have:

3λ = d sinθ

Dividing the two equations, we get:

sinθ = (3/8) sin(63.4°)

θ = sin⁻¹(3/8 sin(63.4°))

θ ≈ 19.6°

Therefore, the third-order maximum occurs at an angle of 19.6°. The answer is (C).

Laser Light Sent Through a Double Slit Produces an Interference