Answer :
Answer:
Highest order = 6 orders
Explanation:
The formula for maxima of diffraction gratings is given by;
dsin θ = mλ
Where;
λ is the wavelength of the light
d is the distance between slits
θ is the angle between the central axis and the corresponding point
m is the order of the interference
Now, for maximum value of the sine function, let's set sin θ = 1
Thus;
d = mλ
To find d, we are told that the grating has 450 lines per mm = 450 x 10³ lines per m
Thus;
d = 1/(450 × 10³)
d = 2.22 × 10^(-6) m
At λ = 700nm = 700 × 10^(-9)m, we have;
m = d/λ = [2.22 × 10^(-6)]/[700 × 10^(-9)]
m = 3.17 ≈ 3
At,λ = 400nm = 400 × 10^(-9)m, we have;
m = d/λ = [2.22 × 10^(-6)]/[400 × 10^(-9)] = 5.55 ≈ 6
Since the fourth maxima occurs further than 3.17 and the seventh maxima occurs further than 5.55,we can say that number of maxima on each side of the central maximum = 6 - 3 = 3.
Thus,there are 6 orders
The Highest order m that contains the entire visible spectrum from 400 nm to 700 nm should be 6 orders.
Calculation of the highest order:
The formula for maxima of diffraction gratings should be
dsin θ = mλ
here,
λ is the wavelength of the light
d is the distance between slits
θ is the angle between the central axis and the corresponding point
m is the order of the interference
Now, for maximum value of the sine function, let's assume sin θ = 1
Now
d = mλ
= 450 x 10³ lines per m
So,
d = 1/(450 × 10³)
d = 2.22 × 10^(-6) m
At λ = 700nm = 700 × 10^(-9)m, we have;
m = d/λ = [2.22 × 10^(-6)]/[700 × 10^(-9)]
m = 3.17 ≈ 3
Now
At,λ = 400nm = 400 × 10^(-9)m, we have;
m = d/λ = [2.22 × 10^(-6)]/[400 × 10^(-9)]
= 5.55
≈ 6
learn more about spectrum here: https://brainly.com/question/18704022