How Does Changing Wavelength Affect Fringe Spacing in a Double-Slit Experiment?

[frederickcan]

Homework Statement

A double-slit experiment is performed with light of wavelength 600 nm. The bright interference fringes are spaced 1.8 mm apart on the viewing screen. What will the fringe spacing be if the light is changed to a wavelength of 400 nm?

Homework Equations

Fringe spacing equation
delta y = wavelength x L / d

The Attempt at a Solution

I tried to solve the fringe spacing for the wavelength of 600 nm by:

600 x 10^-9 m / .0018 m = 3.33E-4

then

plugged in the 3.33E-4 to solve what the spacing would be for 400 nm by:

dividing 400 x 10^-9 m / 3.33E-4 = 1200000

I think I'm interpreting the fringe spacing equation wrong, and I'm not sure where.

 

[ideasrule]

Check your math; your equations are right, but you made a trivial calculation error.

 

[frederickcan]

The only thing is I'm confused about L. The question didn't provide a value for L, and I have two unknowns (L, and the fringe spacing) so I feel like I'm using the wrong equation. However, because I couldn't find a better equation I set L to 1.

(Also, thank you for your help.)

 

[rl.bhat]

In the problem L and d remain the same. So you can write equation for two wavelengths.
λ1 = x1*L/d...(1)
λ2 = x2*L/d...(2) From the first equation find L/d.
Substitute this value in the second equation.