Question

a diffraction grating has 400 slits in total. would you be able to resolve the sodium doublet in the 3rd order with this grating? explain the wavelengths of the sodium doublet are 589nm and 589.6nm

Question 2

In a diffraction pattern due to double slits, the third order interference maxima falls on the first order diffraction minima. What is the relationship between slot srparation and slit width. Two slits are identical

Answer 1

Question 1

Question 2

In a diffraction pattern due to double slits, the third order interference maxima falls on the first order diffraction minima. What is the relationship between slot srparation and slit width.

The interference maxima occur when,

d sin = m

On the other hand, the condition for a first diffraction minima is given as -

a sin =

Thus, a particular interference maximum with order number 'm' which may coincide with a first diffraction minimum.

Then, the value of 'm' may be obtained as -

(d sin ) / (a sin ) = (m ) / ()

m = d / a

If the wavelength of a light and the location of m-order maximum are known, then the distance between slits may be readily deduced. We know that, diffraction is the bending of waves as they pass by an object or through an aperture.

The condition for maximum intensity is the same as that for a double slit. An angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating.

Mathematically, we have

y = m D / d