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?

 

[member 553083]

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.