Blue light of wavelength 450 nm passes through a diffraction grating with a slit spacing of 0.001 mm and makes an interference pattern on the wall. How many bright fringes will be seen?

A. 1

B. 3

C. 5

D. 7

5 fringes option C

Explanation:

Given:

- The wavelength of blue light λ = 450 nm

- The split spacing d = 0.001 mm

Find:

How many bright fringes will be seen?

Solution:

- The relationship between the wavelength of the incident light, grating and number of bright fringes seen on a screen is derived by Young's experiment as follows:

sin (Q) = n * λ / d

Where, n is the order of bright fringe. n = 0, 1, 2, 3, ...

- We need to compute the maximum number of fringes that can be observed with the given condition and setup. Hence we will maximize our expression above by approximating sin (Q).

sin (Q_max) = 1

Q_max = 90 degree

- Hence, we have:

n = d / λ

- plug values in n = 0.001 * 10^-3 / 450*10^-9

n = 2.222

- Since n order number can only be an integer we will round down our number to n = 2.

- Hence, we will see a pair of bright fringes on each side of central order fringe.

- Total number of fringes = 2*2 + 1 = 5 fringes is total ... Hence, option C