Question

Laser light with a wavelength λ = 680 nm illuminates a pair of slits at normal incidence.

What slit separation will produce first-order maxima at angles of ± 45 ∘ from the incident direction?

Answer 1

The slit separation that will produce first-order maxima at angles of ± 45° for laser light with a wavelength of 680 nm is approximately 0.961 μm in Young's double-slit experiment.

Step-by-step explanation:

To determine the slit separation that will produce first-order maxima at angles of ± 45° from the incident direction for laser light with a wavelength λ = 680 nm, we can use the formula for the positions of maxima in Young's double-slit experiment:

d · sin(θ) = m · λ,

where d is the separation between the slits, θ is the angle of the maximum from the central maximum, λ is the wavelength of the light, and m is the order number of the maximum (m = 1 for the first-order maximum). We are given that λ = 680 nm and θ = 45°. To find d, we rearrange the equation to solve for d:

d = λ / (sin(θ))

Substituting the given values:

d = 680 nm / (sin(45°))

d = 680 nm / (0.7071) ≈ 961 nm or 0.961 μm

The slit separation that will produce first-order maxima at angles of ± 45° is approximately 0.961 μm.