Distance between maxima of two-slit interference

[PhizKid]

Homework Statement

A light of wavelength 500 nm interferes through a two slit experiment on a screen. The distance between the first minimum and fourth minimum is 1.68 cm. Find the distance between the central maximum and first order maximum.

Homework Equations

d*sin(θ) = nλ = Δ

d = distance between slits
Δ = path difference

sin(θ) = tan(θ)
tan(θ) = x / L

x = distance between orders
L = distance between slits and screen

The Attempt at a Solution

We can find the path difference between the first and fourth minimum by:

(3.5)λ which is 0.000175 cm. (I converted 500 nm to 0.00005 cm).

So we can get: $\frac{0.000175 cm}{d} = \frac{1.68 cm}{L} = tan(θ_1) = sin(θ_1)$.

We need to find: $\frac{0.00005 cm}{d} = \frac{x}{L} = tan(θ_2) = sin(θ_2)$

But it doesn't look like we have enough information. How can I solve this? Can I use the ratio d / L to set the equation $\frac{0.000175}{1.68} = \frac{0.00005}{x}$?

 

[barryj]

Things to think about: Does the wavelength of 500 nm really matter? is the distance between minimums the same as between maximums? Is the first order max next to the central max?"

 

[PhizKid]

Things to think about: Does the wavelength of 500 nm really matter? is the distance between minimums the same as between maximums? Is the first order max next to the central max?"

I found the distance between minimums is larger than the distancce between maximums. And no, the first order max is not next to the central max because they are separated by a minimum

 

[barryj]

Of course there is a minimum between the central max and the first order max. If you look at the pattern, I think you would see a central bright line, then a dark line, then another bright line, then a dark line and etc, yes. As I recall, the distances get a little larger as you move further away from the center but I doubt this is of concern here.