Question

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

Answer 1

Answer:

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