Answer:
Only two diffraction orders +1 and -1 are possible
Explanation:
The diffraction net is a system with many uniformly spaced lines, which is described by the expression
d sin θ = m λ m = 1, 2, 3,…
Where d is the spread between the lines, λ the wavelength and m is an integer that corresponds to the order of diffraction, all wavelengths
For this case the spacing is
d = 775 nm
The sodium emission lines are 589.00 nm and 589.59 nm
With this data we can calculate how many diffraction orders are visible
θ = sin⁻¹ (m λ / d)
m = 1
λ1 = 589.00 nm
θ1 = sin⁻¹ (1 589/775)
θ1 = 49.46 °
λ2 = 589.59 nm
θ2 = sin⁻¹ ((1 589.59 / 775)
θ2 = 49.53 °
m = 2
λ1 = 589.00 nm
θ1 = sin⁻¹ (2 589/775)
θ1 = sin⁻¹ (1.5)
This order is not possible because the sin cannot be greater than 1
m = -1
λ1 = 589 nm
θ1 = sin⁻¹ (-1 589/775)
θ1 = -49.46
θ= sin⁻¹ ( -1 589.59/775)
λ2 = 589.59 nm
θ2 = -49.53 °
m = -2
λ1 = 589 nm
θ1 = sin-1 (-2 589/775)
This order does not occur because the breast cannot be greater than 1
Only two diffraction orders +1 and -1 are possible
