Question

Laser light with a wavelength λ = 665 nm illuminates a pair of slits at normal incidence. What slit separation will produce first-order maxima at angles of ± 15 ∘ from the incident direction?

Answer 1

Step-by-step explanation:

To determine the slit separation that will produce first-order maxima at angles of ±15 degrees from the incident direction, we can use the equation for the location of the maxima in a double-slit interference pattern:

dsinθ = mλ

Where:

d is the slit separation,

θ is the angle of the maxima from the incident direction,

m is the order of the maxima (in this case, m = 1),

and λ is the wavelength of the laser light.

We need to find d, so we rearrange the equation:

d = (mλ) / sinθ

Given:

λ = 665 nm (or 665 × 10^-9 meters)

θ = 15 degrees (or 15 * π / 180 radians)

m = 1

Substituting the values into the equation:

d = (1 * 665 × 10^-9 m) / sin(15 * π / 180)

Calculating sin(15 * π / 180):

sin(15 * π / 180) ≈ 0.25882

Now, we can calculate the slit separation:

d ≈ (1 * 665 × 10^-9 m) / 0.25882

Simplifying:

d ≈ 2.568 × 10^-6 meters

Therefore, the slit separation that will produce first-order maxima at angles of ±15 degrees from the incident direction is approximately 2.568 μm (micrometers).