Maximizing Single Slit Diffraction: Solving for the Largest Width Without Minima

[bcjochim07]

Homework Statement

Light from a helium neon laser with wavelength 633nm is incident on a single slit. What is the largest slit width for which there are no minima in the diffraction pattern?

Homework Equations

The Attempt at a Solution

For single slit diffraction, asin(theta)=p*lambda, where a= slit width, and p= 1,2,3...


So I know that when the slit width is smaller than the wavelength, no minima occur, but ?
what about when it is equal?

I'll try out some numbers: say the slit width is 6.33e-7 m, the same as the wavelength. Then I will find the angular position of the first minimum:

(6.33e-7)sin(theta)=(1)(6.33e-7)t
theta has to be equal to 90 degrees, which I don't think can be possible. So the wavelength has to be less than 633 nm.

Is this correct?

 

[bcjochim07]

Actually, I think that when the slit width is equal to the wavelength, then the light spreads to fill the region behind the opening. Therefore, I think that the largest the wavelength can be is 633 nm.