Green light of wavelength 500 nm is incident normally on a diffraction grating that has 5300 lines/cm.The second-order image is diffracted at an angle from the normal of
A)10º
B)16º
C)32º
D)48º
E)57º

Question

Quizplus · Accepted Answer

The equation for diffraction on a grating is: 
d sinθ = mλ
where 
d = distance between adjacent slits
θ = angle of diffraction
m = order of diffraction
λ = wavelength of light

Using the given values:
d = 1 / (5300 lines/cm) = 1.8868 x 10^-4 cm
m = 2
λ = 500 nm = 5 x 10^-5 cm

Substituting into the equation, we get:
d sinθ = mλ
1.8868 x 10^-4 cm x sinθ = 2 x 5 x 10^-5 cm
sinθ = 0.53
θ = sin^-1(0.53) = 32º

Therefore, the answer is C) 32º.

Green Light of Wavelength 500 Nm Is Incident Normally on a Diffraction