Question

A grating has 7100 slits/cm. How many full spectral orders can be seen (400 to 700 nm) when it is illuminated by white light?

Express your answer as an integer.

m =

full spectral orders

Answer 1

The formula use would be , n(lambda) = d sin(tethre),

d is the grating space and n is the number of order.

In order to know the maximum number of order,

sin(tethre) must be maximum, that is sin(tethre) = 1

That means ,

n(lambda) = d (1)
n = d / (lambda)

d = 1/7100 = 1.408 x 10^-4 cm = 1.40 x 10^-6 m

Take (lambda) = 400nm,
n = ( 1.40 x 10^-6) / (400 x 10^-9) = 3.5

Take (lambda) = 700nm,
n = (1.40 x 10^-6) / (700 x 10^-9) = 2

Therefore, the number of order for (lambdas) between 400nm to 700nm would be between 2 to 3.

So, the complete spectra order that can be seen is only 2. Because for lambda 700nm, it has two order, while others have more than 2 For a complete spectral order, all must be included.