Answer:
N = 221.4 lines / mm
Explanation:
Given:
- The wavelength of the source λ = 670 nm
- Distance of the grating from screen B = 40.0 cm
- The distance of first bright fringe from central order P = 6.0 cm
Find:
How many lines per millimeter does this grating have?
Solution:
- The derived results from Young's experiment that relates the order of bright fringes about the central order is given by:
sin (Q) = n*λ*N
Where,
n is the order number 0, 1 , 2, 3 , ....
λ is the wavelength of the light source
Q is the angle of sweep respective fringe from central order
N is the number of lines/mm the grating has
- We will first compute the length along which the light travels for the first bright fringe:
L^2 = P^2 + B^2
L^2 = 40^2 + 6^2
L^2 = 1636
L = 40.45 cm
- Now calculate the sin(Q) that the fringe makes with the central order:
sin (Q) = P / L
sin (Q) = 6 / 40.45
- Now we will use the derived results:
N = sin(Q) / n*λ
Where, n = 1 - First order
Plug values in N = (6 / 40.45) / (670 *10^-6)
N = 221.4 lines / mm
