Double Laser Interference: Solving for Small Angles

[jegues]

Homework Statement

See figure attached for problem statement as well as my attempt

Homework Equations

The Attempt at a Solution

I don't know where to go from here. Can someone help me get started?

 

[Redbelly98]

Single slit diffraction . . . there is a standard formula for this. Look in your textbook.

 

[jegues]

Single slit diffraction . . . there is a standard formula for this. Look in your textbook.

I'm aware but I don't know how to deal with two separate lights at the same time, who's wavelength are different.

Can you clarify that portion?

 

[ehild]

The diffraction patterns are also separate, independent of each other.

ehild

 

[jegues]

The diffraction patterns are also separate, independent of each other.

ehild

I'm still having a really tough time with this problem. All I can identify is that,

$$dsin\theta_{r} = m\lambda_{r}$$

and

$$dsin\theta_{g} = n\lambda_{g}$$

so,

$$m\lambda_{r} = n\lambda_{g}$$

Where m = 3, so n =3.5 therefore the nearest minimum would be at 3 for the green laser.

Now how can I calculate the difference between these two minimum on the screen?

Any help would be greatly appreciated, I'm really lost.

 

[ehild]

Find the distances from L and sin(theta).

ehild

 

[jegues]

Find the distances from L and sin(theta).

ehild

I don't understand where sin(theta) is situated.

I know that L is the distance between the screen and the slit but where is sin(theta)?

Theta is the angle in the triangle like so, correct?

I don't know where sin(theta) is so I'm having trouble finding the distance between that and L.

One could say that sintheta is simply opposite over hypotenuse, but I don't know either of those sides.

 

[ehild]

Theta is the angle of the diffracted beam with respect to the central beam.

See : http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/sinslitd.html#c1

ehild

 

[Redbelly98]

Also, at small angles (as occur in this problem), θ, sinθ, and tanθ are all approximately equal to each other.