Question

A diffraction grating is illuminated at normal incidence at an angle 45degree a certain order of light if wavelength 500nm is superimposed with a light of another wavelength of 400nm of next higher order

Answer 1

Answer:

Explanation:

parallel rays of monochromatic radiation, from a single beam in the

form of rays 1 and 2, are incident on a (blazed) di↵raction grating at an angle ✓i

relative to the grating normal. These rays are then di↵racted at an angle ✓r.

We use a negative sign here based on our convention of angle definition. That is,

positive angles are measured to the left of the grating normal, negative angles to

the right. From this figure we can see that ray 2 travels a greater distance than

ray 1. This overall di↵erence can be computed by subtracting the increase in path

lengths from rays 1 and 2.

We can analyze this in more detail by examining Figure 2. Here we represent

the change in path lengths for beams 1 and 2 as

i = d sin ✓i (1)

r = d sin(✓r) = d sin ✓r (2)

Thus the total di↵erence in path length is

T = d sin ✓i  (d sin ✓r) = d(sin ✓i + sin ✓r) (3)

For constructive interference to occur this di↵erence must equal and integer

multiple of the wavelength, . That is

T = m