An 11-mm wide diffraction grating has rulings of 550 lines per mm. Light is incident normally
on the grating. The longest wavelength that forms an intensity maximum in the fifth order is
closest to?
The correct answer is 488nm but I cant seem to get that answer.
To find the longest wavelength that forms an intensity maximum in the fifth order for a diffraction grating, we can make use of the formula:
dsinθ = nλ
Where:
d is the spacing between the rulings of the grating,
θ is the angle at which the intensity maximum occurs,
n is the order of the maximum,
and λ is the wavelength of light.
In this case, the spacing between the rulings (d) is given as 11 mm, and the number of lines per mm is given as 550.
To find the spacing between the rulings (d) in terms of micrometers, we can use the formula:
d = 1 / L
Where:
L is the number of lines per unit length (550 lines per mm).
Therefore, d = 1 / 550 mm = 0.00182 mm = 1.82 μm.
Since the light is incident normally on the grating, the angle θ is 0 degrees.
Now, we can rearrange the formula to solve for λ:
λ = dsinθ / n
For the fifth-order maximum (n = 5), we have:
λ = (1.82 μm)(sin(0 degrees)) / 5
Since sin(0 degrees) is 0, the wavelength will be 0. Therefore, it seems there may be an error in the question or solution provided.
Please double-check the given information or provide additional details if available.