Double slit fringe visibility with sunlight

[Heidi]

Hi Pfs,

I know that Young made his double slits experiment with sunlight and i would like to know the best value of the fringe visibility on the screen.
The visibility is equal to (Imax - Imin)/(Imax + Imin)
thanks

 

[anuttarasammyak]

How do you think of it?

I assume, as sunlight is made of different color lights, blue light makes blue fringe and red light makes red fringe in position slightly outer of blue or so.

Ref.

 

[Heidi]

So the fringe visibility is reduced. I would like to find a numerical value for that. Is it the only thing that reduces the fringe visibility?
Young saw them. the visibility has not to be very little.

 

[sophiecentaur]

i would like to know the best value of the fringe visibility on the screen.

I'm not sure that your formula will help you without more information.
As @anuttarasammyak says, you need to consider the effect of the longer wavelength fringes on the shorter wavelength fringes. It would be best to integrate the level of light at a particular angle over all visible wavelengths.
The level the thread is 'I' so that means you should be able to use the formula in this link to get the family of fringes for each wavelength and find the net max and min values. (Summing for a few spot values would do or you could stick with the formula and integrate over wavelength range).

As you depart from the boresight, the spread due to wavelength range will reduce the visibility until the blue fringes fill in the red fringes and the visibility will (could) be zero.

 

[Heidi]

Thank you for the link. I have another question about the historical experiment by Young. I suppose that he did not use filters to have a monochromatic light. a value for his fringe visibility?

 

[sophiecentaur]

I suppose that he did not use filters to have a monochromatic light. a value for his fringe visibility?

I don't know the precise history of research around that time but Newton used a prism to select wavelength bands. Young could have done it that way to provide a fair monochromatic source if he needed to.
Also, the first one or two fringes are not too bad with sunlight, bearing in mind the fact that perception of the blue end of the spectrum is relatively low, so the effective range of wavelengths would be less than the full visible band.

If you want a theoretical value then do the sums in my last link for different wavelengths to find how wavelength affects your simple formula.

About historical Physics experiments: the guys in the past used to spend a long time on their experiments (servants took care of other aspects of their lives. Young would have ben able to perform a 'filtering operation' by looking just at narrow bands of colour. If you're after a really good answer to your question then you'd need to read Young's actual journals. I'm sure Google would tell you where to find them.

 

[Andy Resnick]

Hi Pfs,

I know that Young made his double slits experiment with sunlight and i would like to know the best value of the fringe visibility on the screen.
The visibility is equal to (Imax - Imin)/(Imax + Imin)
thanks

After spectrally filtering sunlight (say, using green light only), the fringe visibility will vary with slit spacing. The details (van Cittert-Zernike theorem) can be found in, for example, Wolf's "Introduction to the theory of coherence and polarization of light", one basic result is that the fringe visibility will vary (approximately)as a |jinc| (|J_1(x)/x|) function. For sunlight the first zero of fringe visibility corresponds to a slit spacing of about 0.06mm (for green light).