What is the Angular Width of the First Bright Fringe?

[TheLegace]

Homework Statement

A double-slit with a separation of 2.1 μm is used with white light. Find the angular width of the first
bright fringe between the violet (lviolet = 400 nm) and red (lred = 750 nm) end of the spectrum. (Assume
two significant digits.)

Homework Equations

What exactly are the wavelengths I am using. I am a bit confused.

The Attempt at a Solution

I know the it is the first bright fringe. n=1, d = 2.1um w=?
I am not sure what wavelengths to use.

The formula that I think I could use is

sinӨn=nλ/w

I just don't know where to continue.

 

[Doc Al]

I know the it is the first bright fringe. n=1, d = 2.1um w=?
I am not sure what wavelengths to use.

The wavelengths are given. You'll need them both.

The formula that I think I could use is

sinӨn=nλ/w

In this formula, "w" is the slit separation, which you called "d" above. λ is the wavelength.

 

[TheLegace]

What exactly is the angular width, isn't it the w variable.

If not then what is d for?

Now I am a bit confused.

 

[Doc Al]

To avoid confusion, I'd use this formula: sinӨ=nλ/d. This formula gives you the angle made by the nth bright fringe, given the wavelength and slit separation. Find the angle for the first bright fringe formed by each given wavelength. The difference of those angles will be a measure of the "width" of the bright fringe formed by white light.