A single slit illuminated by light of wavelength λ = 610 nm produces a diffraction pattern with its first minimum at 3.5 mm from the central maximum. (a) Find the slit width, and (b) For the same slit, what wavelength of light would produce a first minimum at θ = 4.0 degrees.
D = slit width
m = minima order
L = distance from the slit to the wall
D sin θ = m λ
tan θ = sin θ = θ (small angle approximation)
The Attempt at a Solution
λ = 610 nm or 6.1 x 10^-7 m
m = 1 (first order minima)
x = 3.5 mm (which is the distance from the central maximum to the first minimum)
tan θ = x / L
D = m λ / sin θ
I would be able to solve this question if I was given either the distance from the slit to the wall (L) or the angle (θ), however, I am not given any of this, and as such, I am unsure how to proceed.