Question

Light of wavelength 570.00 nm is incident normally on a diffraction grating, and the third‑order maximum is observed to be 24.0∘ from the normal. How many slits per millimeter are marked on the grating?

Answer 1

Answer : The number of slits per millimeter marked on the grating are 238 slits/mm.

Explanation :

First we have to calculate the slit separation.

Formula used for a diffraction grating when maxima occur:

`d* \sin(a)=n* \lambda`

where,

d = slit separation = ?

a = angle =
`24.0^o`

`\lambda` = wavelength = 570.00 nm

n = order = 3

Now put all the given values in the above formula, we get:

`d* \sin(24.0^o)=3* 570.00nm`

`d=4204.19nm=4.20* 10^(-3)mm`

Conversion used :
`(1nm=10^(-6)mm)`

Now we have to calculate the number of slits per millimeter.

`\text{Number of slits per millimeter}=(1)/(d)`

`\text{Number of slits per millimeter}=(1)/(4.20* 10^(-3)mm)`

`\text{Number of slits per millimeter}=238.09slits/mm\approx 238slits/mm`

Therefore, the number of slits per millimeter marked on the grating are 238 slits/mm.