Double Slit and coherence of non-point source

[jmm5872]

If a "line" source of visible light is not really a line but has a width of 1mm, how far must it be from a double slit which it illuminates in order for the two slits to be reasonably coherent? Assume the slit separation is .5mm.

I approached this problem the same as finding the distance needed for two light sources to be coherent.

Let the line between the two sources be perpendicular to the line from source 1 to the point P, and assume that L_1P and L_2P are parallel and approximately equal to a length L.

We also need L_2P to not exceed L_1P by 1/2 a wavelength.

Then I rearranged the pythagorean formula and used the above criteria to get this formula.

L=(L₁₂)²/wavelength

But I don't think this is the whole picture. I haven't included the .5mm slit width anywhere. Since the slit width is 1/2 the laser width does this mean that the screen containing the slits can be 1/2 the distance L of the above formula?

 

[jbsteele]

Or does the slit width play no role in the equation?The slit width does play a role in this equation. To calculate the distance needed for the two slits to be reasonably coherent, we must take into account the wavelength of the light source and the slit separation. The distance L is given by the following formula: L = (L12 + (slit separation/2))2/wavelength where L12 is the distance between the two light sources. This formula takes into account the slit separation and ensures that the two slits are reasonably coherent.