Question

Using a wavelength laser, you form the diffraction pattern of a wide slit on a screen. You measure on the screen that the dark fringe is away from the center of the central maximum. How far is the screen located from the slit?

Answer 1

y = λ L/ a

Step-by-step explanation:

The diffraction pattern of a single slit is side for the case of destructive interference by

a sin θ = m λ

Where a is the width of the slit, lm the wavelength and m an integer

In general the screen is much larger than the width of the spectrum, so the sine can approach the tangent

sin θ = tan θ = y / L

Substituting remains

a y / L = m λ

y = m λ L /a

For the first dark strip m = 1

y = λ L/ a