Wave Optics - Single Slit Diffraction

[Alice-Shallom]

Light of wavelength 600nm falls on a 0.40-mm-wide slit and forms a diffraction pattern on a screen 1.5m away.
(a) Find the position of the first dark band on each side of the central maximum.
(b) Find the width of the central maximum


For the (a) I think that we use sinθ = +- λ / α
I think m is equal to : m = +- 1

Where λ = 600 nm
and α = 0.40 mm


If the way I have solved (a) is correct, then how do I proceed to (b) ? I know L is 1.5m then what?

[turin]

You use trig. That θ in the equation is the angle for a particular right triangle. There should be a picture in your book. L is one leg and the width of the central max is twice the other leg.

Actually, that equation you used for (a) may need an adjustment. I'll get back to you.

I think that destructive interference occurs for the condition:

(α/2) sinθ = λ/2

Oh, sorry. You just manipulated it. The way you have it should be correct. :redface: