What happens if the monochromatic source is replaced by a source of white light in Young's double slit experiment?
Answers
To analyse the interference pattern, we calculate the intensity of the bright and dark fringes in the interference pattern for harmonic waves. Refer to Figure which is schematic representation of the geometry of Young’s experiment. The phenomenon of interference arises due to superposition of two harmonic waves of same frequency and amplitude but differing in phase.
Let the phase difference between these two waves be δ. We can write y1 and y2 , the displacements at a fixed point P due to the two waves,
as y1=asinwt
and y2=asin(wt+δ)
where δ signifies the phase difference between these waves.
Note that we have not included the spatial term because we are considering a fixed point in space.
According to the principle of superposition waves, the resultant displacement is given by y=y1+y2
= asinwt+asin(wt+δ)
= a[sinwt+sin(wt+δ)]
= 2asin(wt+δ2)cos(−δ2)
= Asin(wt+δ2)
where amplitude of the resultant wave is given by instruments
A= 2acosδ2
The intensity of the resultant wave at point P can be expressed as
I∝A2∝4a2cos2(δ2)---(1)
To see the dependence of intensity on the phase difference between the two waves, let us consider the following two cases.
Case 1 : When the phase difference, δ=0,2π,4π,...,2nπI=4a2cos20
= 4a2
Case 2 : When, δ=π,3π,5π,....,(2n+1)πI=4a2cos2δ2=0
From the results we can conclude that when phase difference between superposing wave is an integral multiple of 2π, the two waves arrive at the screen 'in-phase' and the resultant intensity (or the brightness) at those points is more than that due to individual waves (which is equal to 4a2). On the other hand, when phase difference between the two superposing waves in an odd multiple of π, the two superposing waves arrive at the screen 'out of phase'. Such points have zero intensity and appear to be dark on the screen.
Answer:
So if monochromatic light in Young's double-slit experiment is replaced by white light, then the waves of every wavelength form their separate interference patterns. ... Hence the waves of all colors reach a middle point R in the same phase. So the central fringe is white.