Determining wavelength of double slit experiment

[mitch987]

Homework Statement

If i have the intensity pattern of a double slit experiment and aim to find the wavelength of the monochromatic light incident on the slits with the following information,
- width of each slit
- distance to the screen
- intensity pattern (displacement Vs intensity)

Homework Equations

for double slit (bright fringes):
sin $$\theta$$ = $$\frac{m \lambda}{d}$$

where m is the order of the bright fringe, d is the slit separation

for single slit (dark fringes):
sin $$\theta$$ = $$\frac{m \lambda}{a}$$

where m is the order of the dark fringe, a is the slit width

The Attempt at a Solution

Since the double slit intensity pattern is modulated by the single slit intensity pattern is it possible to use the single slit equation and let a = the slit width?
Since for the double slit equation i have an unknown $$\lambda$$ and unknown d (slit separation).

any help would be greatly appreciated.
Thanks,

 

[anathema]

Thank you for your question. Your approach is correct. In order to find the wavelength of the monochromatic light incident on the slits, you can use the single slit equation and let a be the slit width. This will allow you to solve for the wavelength, as well as the slit separation, which is the other unknown in the double slit equation.

You can also use the double slit equation to verify your results, as the intensity pattern of the double slit experiment is indeed modulated by the single slit intensity pattern. This means that the bright fringes of the double slit experiment will occur at the same angles as the dark fringes of the single slit experiment.

I hope this helps. If you have any further questions, please don't hesitate to ask.