Question

A diffraction grating has 25,000 lines/cm and is illuminated with light having a frequency of 5.0 x 10​14​ Hz. What are the angles of (a) the first-order bright fringe and (b) the second-order bright fringe?

Answer 1

v = speed of light = 3 x 10⁸ m/s

f = frequency = 5.0 x 10¹⁴ Hz

= wavelength = ?

wavelength is given as

= v/f

= (3 x 10⁸)/(5.0 x 10¹⁴)

= 6 x 10^-7 m

d = width of the slit = 0.01/25000 = 4 x 10^-7 m

a)

= ?

n = 1

for bright fringe

d Sin = n

Sin = n /d

Sin = (1) (6 x 10^-7)/(4 x 10^-7)

Sin = 1.5

Since value of Sin can not be greater than 1, hence angle for first-order bright fringe is not possible

b)

= ?

n = 2

for bright fringe

d Sin = n

Sin = n /d

Sin = (2) (6 x 10^-7)/(4 x 10^-7)

Sin = 3

Since value of Sin can not be greater than 3, hence angle for first-order bright fringe is not possible