Calculate the number of lines per cm of a grating which gives an angle of diffractionequal to 30 o in the first order of light of wavelength 600nm.

To solve this problem, we will use the grating equation which is given by:

dsin(θ) = mλ

where: d is the distance between the slits (or lines) in the grating, θ is the angle of diffraction, m is the order of diffraction, and λ is the wavelength of the light.

We are asked to find the number of lines per cm, which is the reciprocal of d. So, we need to rearrange the grating equation to solve for d first.

From the grating equation, we have:

d = m*λ / sin(θ)

Substituting the given values:

d = 160010^-9 m / sin(30°) d = 60010^-9 m / 0.5 d = 120010^-9 m d = 1.2*10^-6 m

Now, to convert d to lines per cm, we take the reciprocal and convert from meters to centimeters:

Lines per cm = 1/d * (1 m/100 cm) Lines per cm = 1/(1.2*10^-6 m) * (1 m/100 cm) Lines per cm = 833.33 lines/cm

So, the grating has approximately 833 lines per cm.