Distance between two second order maxima

[kuzco890]

Homework Statement

Monochromatic light strikes a diffraction grating at normal incidence before illuminating a screen 1.99 m away. If the first-order maxima are separated by 1.36 m on the screen, what is the distance between the two second-order maxima?

Homework Equations

I think these are the relevant equations:
deltaL = dsinθ
y = Ltanθ

The Attempt at a Solution

L = 1.99 m
I'm not sure where the 1.36 and 1.99 come in.

 

[Delphi51]

Take a look at http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/grating.html#c2
You'll see the formula you need (with a sine theta in it) and it shows how the first order (m=1) and second order (m=2) maxima appear.

 

[kuzco890]

So I only need the d sinθ = mλ equation?
Would you be able to help walk me through it?
I feel like I need the y = Ltanθ or deltaL = dsinθ equation.
Doesn't L = 1.36 for the first order maxima?
d = 1.99 m
m = 2?

 

[Delphi51]

Draw the triangle with theta, x (distance from center to maximum - half the 1.36), L (L is the hypotenuse), and the 1.99 m distance to the screen. Use the triangle and some trig to find theta.

Use the formula to find lambda/d. This value doesn't change as you move to 2nd order, so you can use the formula again with this value to find theta when m = 2.

 

[kuzco890]

Thanks!