Question

Light of wavelength 650 nm is normally incident on the rear of a grating. The first bright fringe (other than the central one) is at an angle of 5 ° with respect to the normal.

1)Find the number of slits per centimeter in the grating.


_________slits/cm


2)Two rays of light of wavelength 650 nm and 420 nm are normally incident on a different grating. If the grating has 5000 slits/cm, what is the angular seperation of of the two light rays' second order maximum.


|θ650 -θ420| =_________°

Answer 1

given,

wavelength (λ) = 650 nm

angle = 5°

using bragg's law

`sin \theta = (n \lambda)/(d)`

`d= (n \lambda)/(sin \theta)`

`d= (1 * 650 * 10^(-9)\ m)/(sin5^0)`

d = 7.46 x 10⁻⁴ cm

number of slits per centimeter

=
`(1)/(d)\\\Rightarrow (1)/(7.46* 10^(-4))\\\Rightarrow 1340 split per centimeter.`

b) wavelength of two rays 650 nm and 420 nm

`d = (1)/(5000)`

d = 2 x 10⁻6 m

we now,

`sin \theta = (n \lambda)/(d)`

for 650 nm

`sin \theta = (2* 650* 10^(-9))/(2* 10^(-6))`

`\theta =sin^(-1)(0.65)`

θ = 40.54°

for 450 nm

`sin \theta = (2* 450* 10^(-9))/(2* 10^(-6))`

`\theta =sin^(-1)(0.45)`

θ = 24.83°

now, difference

|θ_{650} -θ_{420}| =40.54°-24.83°

|θ_{650} -θ_{420}| =19.71°