Question

A student shines a monochratic light through a diffraction grating with 4,000 lines per cm. the distance between the grating and the screen is 1.2 m. The student measures the distance between the first order fringe and central maxima at 0.2cm. What is the frequency of the monochromatic light? Show work.

Answer 1

y = distance between the first order fringe and central maxima = 0.2 cm

D = screen distance = 1.2 m = 120 cm

for small angles

Sin tan = y/D = 0.2/120 = 0.00167

= wavelength = ?

d = 0.01/4000 = 2.5 x 10^-6 m

using the equation

d Sin = m

m = 1

(2.5 x 10^-6 ) (0.00167 ) = (1)

= 4.175 x 10^-9 m

c = speed of light = 3 x 10⁸ m/s

frequency is given as

f = c/

f = (3 x 10⁸)/(4.175 x 10^-9)

f = 7.2 x 10¹⁶ Hz