© examsnet.com
Question : 28
Total: 30
(a) (i) 'Two independent mono-chromatic sources of light cannot produce a sustained interference pattern'. Give reason
(ii) Light wave each of amplitude 'a ω y 1 = a cos ω t y 2 = a cos ( ω t + ϕ ) ϕ
(b) In Young's double slit experiment, using monochromatic light of wavelengthλ λ K
OR
(a) How does one demonstrate, using a suitable diagram, that unpolarised light when passed through a polaroid gets polarized?
(b) A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarised, whenµ = tan i B µ i B
(ii) Light wave each of amplitude '
(b) In Young's double slit experiment, using monochromatic light of wavelength
OR
(a) How does one demonstrate, using a suitable diagram, that unpolarised light when passed through a polaroid gets polarized?
(b) A beam of unpolarised light is incident on a glass-air interface. Show, using a suitable ray diagram, that light reflected from the interface is totally polarised, when
Solution:
(a) (i) The condition for the sustained interference is that both the sources must be coherent (i.e., they must have the same wavelength and the same frequency, and they must have the same phase or constant phase difference).
Two sources are monochromatic if they have the same frequency and wavelength. Since, they are independent, i.e., they have different phases with irregular difference, they are not coherent sources.
Let the displacement of the waves from the sourcesS 1 S 2 P t
y 1 = a cos ω t
andy 2 = a cos ( ω t + ϕ )
Where,ϕ
By the superposition principle, the resultant displacement at pointP
y = y 1 + y 2
y = a cos ω t + a cos ( ω t + ϕ )
y = 2 a [ cos (
) cos (
) ]
y = 2 a cos ( ω t +
) cos (
)
Let2 a cos (
) = A
Then, equation (i) becomes
y = A cos ( ω t +
)
Now, we have:
A 2 = 4 a 2 cos 2 (
)
Then intensity of light is directly proportional to the square of the amplitude of the wave. The intensity of light at point on the screen is given by
I = 4 a 2 cos 2
(b) Intensity I = 4 I 0 cos 2
When path difference isλ 2 π
I = 4 I 0 cos 2 π
= 4 I 0 = k
When path difference,∆ =
ϕ 1 =
∆
=
×
=
I 1 = 4 I 0 ⋅ cos 2
( since k = 4 I 0 )
= k cos 2
= k × ( −
) 2
=
k
Two sources are monochromatic if they have the same frequency and wavelength. Since, they are independent, i.e., they have different phases with irregular difference, they are not coherent sources.
Let the displacement of the waves from the sources
and
Where,
By the superposition principle, the resultant displacement at point
Let
Then, equation (i) becomes
Now, we have:
Then intensity of light is directly proportional to the square of the amplitude of the wave. The intensity of light at point on the screen is given by
(b)
When path difference is
When path difference,
© examsnet.com
Go to Question: