# Homework Help: Finding separation of bright spots

1. May 6, 2013

### omc1

1. The problem statement, all variables and given/known data A scientist decides to do the double-slit experiment in a vertical tube, with the slits at the top and a viewing screen at the bottom as shown. With red light from a HeNe laser (632 nm) a nice pattern forms on the viewing screen, with the bright spots 1.00 cm apart.
Now the scientist fills the tube up with water. What is the separation of the bright spots now?

2. Relevant equations i used v=c/n v=λf y=m(λ)L/d

3. The attempt at a solution λ=c/nf plugged that into y(initial)=m(λ)L/d, i used 1.33 as the index number. y(final)=m(λ)L/d to find the new separation, the m, L, d cancel out leaving y=λ or y(final)=c/nf c=3x10^8, n=1.33, f=632x10^-9 meters, i got 3.5x10^14 which seems to me to be really large...please help its due tonight, thanks!

2. May 6, 2013

### rude man

Optical path difference changes from d sin(theta) to n*d sin(theta) = m(lambda). Careful about lambda in water ....

3. May 6, 2013

### omc1

wait, i dont see how that equation applies here? i dont see how sin(theta) works here?

4. May 7, 2013

### haruspex

But the lambdas are different, right?
I don't understand how you arrived at that. y is the band separation, lambda is the wavelength of the light. Why should they be equal?
f is frequency, surely, not wavelength.

5. May 7, 2013

### rude man

In air:
If θm is the angle subtended at maximum number m, then d sin θm = mλ.

In water:
if θ'm is the angle subtended at maxium number m, then n*d sinθ' = mλ'.

For both air and water, for m = 0 we get the center maximum. For m = 1 we get the first separation.

The ratio of sinθ'm/sinθm is the same as the ratio of screen spacings in air vs. in water.

You know n, λ and λ' so you know the sine ratio and therefore the spacing ratio. Use m = 1 for the spacings for both cases.