Question

Q24
Light of wavelength 450 nm is incident on a diffraction grating on which 5000 lines/cm have been ruled.
How many orders of spectra can be observed on either side of the direct beam?
A
1
B
2
с
3
d
4

Answer 1

Answer:

The equation for the diffraction is

n

λ

=

d

sin

θ

The wavelength of the light is

λ

=

600

⋅

10

−

9

m

The width of a line is

d

=

1

5000

⋅

100

m

The maximum value for

sin

θ

=

1

Therefore,

n

=

d

sin

θ

λ

=

0.2

⋅

10

−

5

6

⋅

10

−

7

=

0.033

⋅

10

2

=

3.33

≃

3

The highest order is

=

3

Answer 2

Given :Light of wavelength of Light = 450 nm

           diffraction grating =  5000 lines/cm

To Find : Orders of spectra on either side of the direct beam observed

Explanation:

The equation for the diffraction is

nλ = d sin θ

          Where,

          n is the order of grating,

         d is the distance between two fringes or spectra

          λ is the wavelength of light

         θ is the angle to maxima

The wavelength of the light is

λ =  600 nm = $\[6 \times {10^{ - 7}}m\]$  

The width of a line is

d = $\[\frac{1}{{5000}}cm\]$ = $\[2 \times {10^{ - 6}}\]$  

The maximum value for

sin θ  =  1

Therefore,

nλ = d sin θ

n = $\[\frac{{d{\text{ }}sin{\text{ }}\theta }}{\lambda }\]$                                    (for maximum value sin θ  =  1)

n = $\[\frac{{2 \times {{10}^{ - 6}}}}{{6 \times {{10}^{ - 7}}}}\]$  

n = $\[\frac{{20}}{6}\]$

n = 3.3333 ≃  3

The highest order is =  3

Hence, Orders of spectra on either side of the direct beam observed is 3