Light with a wavelength of λ = 614 nm is shone first on a single slit of width w = 3.75 μm. the single slit is then replaced with a double slit separated by a distance w. the ratio of the single slit angle to the double slit angle for the first dark fringe is rθ.find the ratio between these angles numerically.

The ratio, is 2

Solution:

As per the question:

Wavelength,

Single slit width, w =

Now,

We know from the eqn for diffraction:

Now,

For single slit:

n = 1

For very small angle:

≈

             (1)

For double slit:

n = 2

Thus

For very small angle:

≈

            (2)

For the ratio, , we divide en (1) by eqn (2):

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