Dark fringes in the bright fringes while doing Young's double-slit experiment

Question

The above image shows the bright and dark fringes that I got while doing Young's double-slit experiment.

Increasing the distance of screen from the slit increases the width of the bright fringes. So when I increased the distance of screen from the slit I got the following enlarged bright fringe.

My doubt's are

1. Why is the central bright fringe in the first image larger than the other bright fringes because fringe width is given by $w={D\lambda\over d}$, which is a constant?

2.Why is there dark fringes in the bright fringe when I move the screen far from the slit.

Answer 1

This is the "expected" result with the intensity of the equally spaced double slit fringes modulated by the diffraction pattern due a single slit.

You will note that the central part of the pattern is massively over-exposed and this might well influence what is happening over the rest of the pattern. Also with the viewing screen closer to the double slits the interference fringes will be closer together.

The problem is to do with the dynamic range of the pattern on the screen and the dynamic range of the camera.

In photography, the dynamic range is the difference between the darkest and lightest intensities in an image. The dynamic range is measured in stops. An increase of one stop equals a doubling of the brightness level. The human eye can perceive about 20 stops of dynamic range in ideal circumstances. This means that the darkest tones we can perceive at anyone time are about $2^{20} \approx 1,000,000$ times darker than the brightest ones in the same scene. This is how you can still see details in dark shadows on a bright, sunny day.

Cameras have a narrower dynamic range than the human eye just under 15 stops ($\approx 30,000$) of dynamic range in any one photo. Most digital cameras get somewhere between 12 and 14 ($\approx 10,000$). This is why when you take photos on a sunny day you often have to choose whether you blow out your highlights, making them pure white (as in your image?), or crush your shadows, making them pure black in the final image.

So when the viewing screen is close to the double slit, the fringes are "there", closer together, but washed out.

Another possibility is that in moving the viewing screen your also moved the double slit / laser and that resulted in the narrow laser beam only illuminating one of the slits.

I am very impressed with your top photograph as getting the contrast right when photographing interference patterns is often very difficult.

Answer 2

How well do you know Fourier theory? The far field diffraction pattern can be obtained as the Fourier transform of the aperture functions. In this case, the aperture function is just two displaced square pulse functions. The Fourier of one square pulse gives a since function, which looks very much like the first image. Two displaced identical functions can be represented by the convolution of the functions by two displaced Dirac delta functions. The Fourier transform of a convolution is the product of the respective Fourier transforms. The Fourier transform of two displaced Dirac delta functions is a cosine function. So the far field diffraction pattern would be a sinc function time a cosine function, which is what you get in your second image. Why don't you see the cosine in the first image? Perhaps because they are to small to notice with the given resolution of the image.