How Does Path Difference Affect Interference Patterns in Light Waves?

[luke949]

Homework Statement

http://img5.imageshack.us/img5/4605/lchuynh177setphys52awee.png

The figure shows the interference pattern that appears on a distant screen when coherent light is incident on a mask with two identical, very narrow slits. Points P and Q are maxima; Point R is a minimum. The wavelength of the light that created the interference pattern is λ = 699 nm, the two slites are separated by rm d = 6 μm, and the distance from the slits to the center of the screen is L = 80 cm . The difference in path length at a point on the screen is ∆s = |s1 − s2|, where s1 and s2 are the distances from each slit to the point.
1. What is ∆s (in nm) at Point P?
2. What is ∆s (in nm) at Point Q?
3. What is ∆s (in nm) at Point R?

Homework Equations

da=sqr(L^2+(D/2+d/2)^2)
db=sqr(L^2+(D/2-d/2)^2)

The Attempt at a Solution

I know the answer to the first problem is 0.
But i tried plugging in da=sqr(80^2+(699-3)^2) and I am getting it wrong. I tried converting all the units to nm, but then the equation just turns into sqr(80nm^2) because the second term turns into a number close to zero.

 

[PeterO]

Homework Statement

http://img5.imageshack.us/img5/4605/lchuynh177setphys52awee.png

The figure shows the interference pattern that appears on a distant screen when coherent light is incident on a mask with two identical, very narrow slits. Points P and Q are maxima; Point R is a minimum. The wavelength of the light that created the interference pattern is λ = 699 nm, the two slites are separated by rm d = 6 μm, and the distance from the slits to the center of the screen is L = 80 cm . The difference in path length at a point on the screen is ∆s = |s1 − s2|, where s1 and s2 are the distances from each slit to the point.
1. What is ∆s (in nm) at Point P?
2. What is ∆s (in nm) at Point Q?
3. What is ∆s (in nm) at Point R?

Homework Equations

da=sqr(L^2+(D/2+d/2)^2)
db=sqr(L^2+(D/2-d/2)^2)

The Attempt at a Solution

I know the answer to the first problem is 0.
But i tried plugging in da=sqr(80^2+(699-3)^2) and I am getting it wrong. I tried converting all the units to nm, but then the equation just turns into sqr(80nm^2) because the second term turns into a number close to zero.

No geometry/trigonometry is necessary.

Think about the requirements for those particular maximum and minimum lines!

 

[luke949]

Hmmmm I am almost positive that the pythagorean Theorem must be used. I can't really see it any way. what do you mean by requirements?

 

[luke949]

Is the answers 1) 0, 2) 699nm, 3) 1048.85? I believe that the the center is a maxima and Q is the next maxima so that is one full wavelength. R is a minima right after the first maxima so it is 699+349.5 = 1048.85nm. Please get back to me thank you.

 

[PeterO]

is the answers 1) 0, 2) 699nm, 3) 1048.85? I believe that the the center is a maxima and q is the next maxima so that is one full wavelength. R is a minima right after the first maxima so it is 699+349.5 = 1048.85nm. Please get back to me thank you.

exactly! They ask for path difference, and the maxima and minima occur for specific path differences

EDIT: I am in East Coast Australia, so time differences will explain any delay in this response.