With the use of the formula SinФ = nλ / d, there are 16 spectral orders which can be seen when it is illuminated by white light.
Given that a grating has 2000 slits/cm. That is,
d = 0.01 / 2000
d = 5 x m
The wavelength λ = (700 - 400) nm
λ = 300 x m
To calculate how many full spectral orders that can be seen (400 to 700 nm) when it is illuminated by white light, we will use the below formula
SinФ = nλ / d
Φ = (nλ / d)
When n = 1
Φ = (300 x
/ 5 x
)
Φ = 3.4 degrees
when n = 2
Φ = (2 x 300 x
/ 5 x
)
Ф = 6.9 degrees
When n = 3
Ф = (3 x 300 x
/ 5 x
)
When n = 16
Ф = (16 x 300 x
/ 5 x
)
Ф = (0.96)
Ф = 73.7 degrees
when n = 17
Ф = (17 x 300 x
/ 5 x
)
Ф = (1.05)
Ф = Error ( that is, it does not exist)
Therefore, there are 16 spectral orders which can be seen when it is illuminated by white light.
Learn more about double slit here: brainly.com/question/4449144