How Do Different Wavelengths Overlap in Double-Slit Interference?

[LegendLen]

Homework Statement

In a double-slit interference experiment the slit separation is 8.40 x 10-6 m and the slits are 2.80 m from the screen. Each slit has a width of 1.20 x 10-6 m.

2 lights of wavelength 450nm and 600nm are shone on the same slits.

If both of the above light sources are shined on the slits at the same time, which order bright fringes from the two light sources would occur at the same locations on the screen? Include the orders of all possible fringes that would overlap.

Homework Equations

dsin

= m

dsin

= (m +0.5)

The Attempt at a Solution

Ok so this is part of a multi-part assignment. Using the equations above I've determined "how far (in meters) from the center of the interference pattern on the screen will the third order (m = 3)" be for the bright (450) and dark (600) fringes separately. The next part of the question asks about shining them at the same time and about bright fringe orders.

My guess was to set both equations equal to each other without m and having both dsin

cancel out leaving m

= (m + 0.5)

and calculating for the order, but I realize this will only give me potentially one answer so I feel like my methods are incorrect.

Could someone give me some guidance about how to approach this question?

 

[vela]

Why are you using the equation with $m+0.5$ in it? Does it even apply to this problem? Don't you also need to keep track of the wavelengths? You seem to be using $\lambda$ to represent both at the same time.

 

[Physics-Tutor]

I agree with Vela, where does this 0.5 come from?
The question is: what is the value of n for which a fringe due to (λ₁) will coincide with that a fringe of λ₂). The first occurrence will occur when one of the wavelength has created an extra fringe compared to the other... (So a difference in fringe order of 1...). Rewrite your equation taking this into account, and find the value of n that will satisfy such condition.
"I realize this will only give me potentially one answer...". You can also explore the case where the difference of order is more than 1, and see if such solution is possible by checking that sin([PLAIN]http://theory.uwinnipeg.ca/physics/light/img32.gif) remains <1