Question

If the distance between slits on a diffraction grating is 0.50 mm and one of the angles of diffraction is 0.25°, how large is the path difference?
nm




How many orders of bright lines does this equal for red light with a wavelength of 650 nm?


wavelengths

Answer 1

Answer:

-  path differnce = 2.18*10^-6

-  1538 lines

Explanation:

- The path difference for the waves that produce the pattern of diffraction, is given by the following formula:

$path\ difference\ = dsin\theta$           (1)

d: separation between slits = 0.50mm = 0.50*10^-3 m

θ: angle of a diffraction = 0.25°

Then, the path difference is:

$path\ difference\ =(0.50*10^{-3}m)sin(0.25\°)=2.18*10^{-6}m$

- The maximum number of bright lines are calculated by using the following formula:

$m\lambda = dsin\theta$           (2)

m: order of the bright

λ: wavelength = 650nm

The maximum bright is calculated for an angle of 90°:

$m=\frac{(0.50*10^{-3}m)sin90\°}{650*10^{-9}m} \approx 769$

The maxium number of bright lines are twice the previous result, that is, 1538 lines

Answer 2

Answer:

a. 2200

b. 3

Explanation: