# Young's double slit experiment - Independent and dependant variables?

1. Aug 6, 2011

1. The problem statement, all variables and given/known data

Hey everyone,

I am doing youngs double slit experiment to find the wavelength of a light source but i am having a lot of trouble finding the independent and dependent variables. Can people suggest what they could be? Thanks. Also, some controlled variables would be helpful aswell.

2. Relevant equations

I use d sin (theta) = m * lamda

3. The attempt at a solution

We measured the fringe separation to calculate the wavelength, so i said it might be:

independent: wavelength of light

dependant: fringe separation

Controlled: NOW I AM CONFUSED. You see, its supposed to be that the wavelength is constant, and hence the fringe separation is constant. I don't know. Can someone please help?

2. Aug 6, 2011

### Delphi51

That is an interesting experiment. I see you measured the fringe separation (usually labeled x or y), so you need a formula with x or y in it. Take a look at this formula derivation:
http://hyperphysics.phy-astr.gsu.edu/hbase/phyopt/slits.html#c1
and be sure you understand all the variables in the formula
y = mλD/d
This is often written x = nλL/d,
but this particular website uses y for the distance from the center to the fringes instead of x, and D for the distance between slits and screen instead of L.
Next, you will want to solve the formula for λ.
If you know all the other values, you can immediately calculate λ.

The independent, dependent and controlled variables come into play when you make an experiment out of this and vary something, hold other things constant, and see what the effect is on another quantity. Say you keep the wavelength, distance between slits and distance to the screen constant (controlled). You vary the fringe number (m is the independent variable) and measure the distance y from the center to each fringe (y is the dependent or responding variable). Then you will have a table of values for m and y. If you graph y versus m, you will have something interesting. If it is a straight line, you can write a formula for it and compare with the theoretical y = mλD/d which has the form
y = km (where k is the slope). If your graph's slope is the same as λD/d (to within experimental accuracy), then you have shown that the formula has some validity.

Of course there are several other experiments you could do. For example, vary the distance to the screen while holding λ, d and m constant and see how y responds to that. In this case D is the manipulated or independent variable, while y is the responding or dependent variable.

It is even more fun if you don't know the formula in advance! Then you can figure out the formula by varying one quantity at a time.