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.
Question
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.
Solution
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 (which is the reciprocal of the number of lines per cm we want to find), θ is the angle of diffraction, m is the order of diffraction, and λ is the wavelength of light.
Given in the problem, we have: θ = 30 degrees, m = 1 (since it's the first order of light), and λ = 600 nm = 600 * 10^-9 m (converting nanometers to meters).
We want to find d, so we rearrange the equation to solve for d:
d = m*λ / sin(θ)
Substituting the given values:
d = 1 * (600 * 10^-9 m) / sin(30 degrees)
Since sin(30 degrees) = 0.5, we have:
d = 1 * (600 * 10^-9 m) / 0.5 d = 1.2 * 10^-6 m
But we want the number of lines per cm, not the distance between the lines. So we take the reciprocal of d and convert from meters to cm:
Number of lines per cm = 1/d * (1 m/100 cm) Number of lines per cm = 1/(1.2 * 10^-6 m) * (1 m/100 cm) Number of lines per cm = 8333.33 lines/cm
So, the grating has approximately 8333 lines per cm.
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