Question

Diffraction grating produces its third-order bright band at an angle of 79.4 ∘ for light of wavelength 791 nm .

Part A

Find the number of slits per centimeter for the grating.

n = 

Part B

Find the angular location of the first-order bright band.

θ1 = 

Part C

Find the angular location of the second-order bright band.

θ2 = 

Part D

Will there be a fourth-order bright band?

Answer 1

The basic equation for calculating the diffraction pattern caused due to the grating is given by,

where, d = distance between the slits, m = order of the band, = wavelength and is the angle.

PART A

To find no of slits per cm, we can calculate the distance between slits from the above data given in the question, it says that at there is third order bright band for wavelength 791 nm,

Therefore number of slits per cm, n is given by,

PART B

Now we have to calculate for band (first order bright band)

Substituting values we get,

Therefore,

PART C

Similarly, for this, we have to calculate for (second order bright band)

Therefore,

PART D

For finding the possibility of having a fourth band in the interference pattern we use the property of ie.

From the diffraction equation, we get,

For the fourth bright band,

Since the value is greater than 1, there will be NO fourth-order bright band in the pattern.