Answer:
m_max = 5
Explanation:
In order to calculate the number of bright fringes on the screen, you first take into account the diffraction grating equation:
[tex]dsin\theta=m\lambda[/tex] (1)
d: distance between slits
m: order of a bright fringe
λ: wavelength of light = 720nm = 720*10^-9m
θ: angle between the normal to the grating and the mth bright fringe
The maximum number of fringes is obtained when the angle θ is a maximum, that is, for θ=90°
The distance between slits is calculated by using the following formula:
[tex]d=\frac{1}{N}[/tex]
N: number of slits per meter = 750 lines/mm
[tex]d=\frac{1}{750lines/mm}=1.333*10^{-3}mm=1.333*10^{-6}m[/tex]
You solve for m in the equation (1)m, and replace the values of d and θ for the maximum number of bright fringes over the normal to the screen.
[tex]m=\frac{dsin\theta}{\lambda}\\\\m=\frac{(1.333*10^{-6}m)sin90\°}{720*10^{-9}m}=1.85[/tex]
The maximum number of bright fringes is an integer, then you approximate m = 2. This means that there are two bright fringes above the central peak.
The total number of fringes is twice the previous value of m plus the central peak:
[tex]m_{max}=2m+1=2(2)+1=5[/tex]
There are 5 bright fringes in the diffraction pattern
