Write intensity as a function of height from centre of screen in YDSE for two coherent light sources of equal intensity
Example: A point source is emitting light of wavelength 6000Ao is placed at a very small height h above a flat reflecting surface MN as shown in the figure. The intensity of the reflected light is 36% of the incident intensity. Interference fringes are observed on a screen placed parallel to the reflecting surface at a very large distance D from it. Find the shape of the interference fringes, on the screen.
Solution: S′ represents the another point source forms due to reflection from the mirror. S′P=(x+h)2+y2 and SP=(x−h)2+y2 Let path difference at point P be Δ Using, Δ+SP=S′P Squaring and adding, Δ2+4hx=−2Δ(x−h)2+y2 Squaring and adding again, Δ4+16h2x2+8hxΔ2=4Δ2(x2+h2−2hx+y2) ⟹4(Δ2−4h2)x2−16Δ2hx+y2+4Δ2h2−Δ4=0 which represents equation of circle as X2+Y2=R2 Thus the fringes will be of Circular shape centered at O.
Problem on maximum and minimum intensity ratio calculation during interference
Example: A point source is emitting light of wavelength 6000Ao is placed at a very small height h above a flat reflecting surface MN as shown in the figure. The intensity of the reflected light is 36% of the incident intensity. Inference fringes are observed on a screen placed parallel to the reflecting surface at a very large distance D from it. Find the ratio of maximum to minimum intensities at P.
Solution: Before reflection, intensity of light is Io(say) and after reflection it becomes 0.36Io Imax=Io+0.36Io+2Io×0.36Io=2.56Io Imin=Io+0.36Io−2Io×0.36Io=0.16Io So, IminImax=16256=16:1
Problems on points on screen with minimum and maximum intensity in YDSE
Example: A screen is placed 2m away from a single narrow slit. Find the slit width if the first minimum lies 5mm on either side of the central maximum. (wave length =5000A∘)
Historically, Young's Double slit experiment, when it was first carried out by Young in 1801, demonstrated that light was a wave, which seemed to settle for once and all the debate whether light was corpuscular (particle-like) or wave. Up until that time, Newton's corpuscular was the prevailing view of light, in spite of alternate explanations such as Huygens' wave front model (which had some serious shortcomings). After Young's demonstration of the wave properties of light, followed by work by others such as Fresnel studying the interference and diffraction properties of it, and especially after Maxwell's brilliant equations of electromagnetism, physicists in the 19th century rejected Newton's corpuscular theory and believed that light was a wave.