Two Offset Slits (help really appreciated)

[dopher]

I'm having trouble getting started with this problem. I know the interference formulas and how it works, but I'm having trouble determining the phase difference.
|----------|------------|
|----------B------------|
|----------|------------|
|----------C------------|
|----------|------------|
A----------|------------O
|----------|------------|
|----------|------------|
|<---x1-->|<-----x2--->|


Consider the above setup, not drawn to scale.

Light of wavelength λ= 475 nm is shined at normal incidence to the first screen with slit A.
The second screen, x1 = 0.7 meters behind the first screen, has two slits, B and C .
The third screen is x2 = 1.5 meters behind the second screen. It has slit O, which is level with slit A. A lightmeter measures the light intensity at the slit O.

When light is sent through slit A and measured at the slit O with either slit B or slit C open one slit at a time, the intensity at the point O is the same: I0 = 0.5 W/m2. (The slit widths can always be adjusted so that this is true, but for this problem you can/should ignore the width of all slits.)

Slit B is at height y1 = 2 mm above slit A.

Slit C is at height y2 = 1 mm above slit A.

Note that the drawing is not drawn to scale.

a) What is the light intensity measured at the point O when both slits B and C are open?

 

[Nate810]

b) What is the phase difference between the light waves passing through slits B and C? a) The light intensity measured at the point O when both slits B and C are open is given by the formula for interference as follows:I = I0 + 2I0cos(2π(y1 - y2)/λ). In this case, y1 = 2mm, y2 = 1mm, and λ = 475nm. Plugging these values into the equation gives us:I = 0.5 + 2(0.5)cos(2π(2 - 1)/475) = 0.78 W/m2. b) The phase difference between the light waves passing through slits B and C can be determined using the formula: Δφ = 2π(y1 - y2)/λ. Substituting the values for y1, y2, and λ gives us Δφ = 2π(2 - 1)/475 = 0.013 radians.

 

[Moetasim]

I would approach this problem by first identifying the key factors involved, which are the wavelength of the light, the distance between the screens and slits, and the height difference between slits B and C. I would also note that the light intensity at point O is the same when either slit B or C is open, and that the slit widths can be ignored for this problem.

Next, I would use the interference formula to determine the phase difference between the two slits. This can be done by finding the path difference between the two slits, which is equal to the difference in distance traveled by the light from each slit to the point O. In this case, the path difference would be equal to the difference in the distances x1 and x2, which is 0.8 meters.

Using the formula for path difference, Δx = (m+1/2)λ, where m is the order of the interference pattern, we can solve for m to find the phase difference between the two slits. Plugging in the given values, we get m = 0.8/0.475 = 1.684.

Since m is a non-integer value, this indicates that there will be a phase difference between the two slits, resulting in interference patterns at point O. The exact intensity at point O when both slits B and C are open can be calculated using the formula I = I0cos^2(πΔx/λ). Plugging in the values, we get I = 0.5cos^2(1.684π) = 0.25 W/m^2.

In conclusion, the light intensity measured at point O when both slits B and C are open is 0.25 W/m^2. It is important to note that this value may change depending on the exact values of the distances and heights given, but the overall approach and use of the interference formula would remain the same.