Figure 35-27a shows the cross-section of a vertical thin film whose width increases downward because gravitation causes slumping. Figure 35-27b is a face-on view of the film, showing four bright (red) interference fringes that result when the film is illuminated with a perpendicular beam of red light. Points in the cross section corresponding to the bright fringes are labeled. In terms of the wavelength of the light inside the film, what is the difference in film thickness between (a) points a and b and (b) points b and d?
(a) The difference in the thickness between points a and b is.
(b) The difference in the thickness between points b and d is.
The expression to calculate the wavelength inside the film is given as follows.
Here, n is the refractive index of the medium, is the wavelength, L is the thickness of the firm, and m is the order of the interference and it can take values 0,1,2,3........
The bright fringes in the thin films produce when 2L is equal to multiple of wavelength.
Substitute for into above equation.
Between points, a and b, the order of the interference is 1. Therefore,
Substitute 1 for m into equation (i).
Hence, the difference in the thickness between points a and b is.
Since between points b and d, the order of the interference is 2. Therefore,
Substitute 2 for m into equation (i)Hence, the difference in the thickness between points b and d is.
In Fig. 35-40, two isotropic point sources of light (S1 and S2) are separated by distance along a y axis and emit in phase at wavelength 900 nm and at the same amplitude. A light detector is located at point P at coordinate on the x axis. What is the greatest value of at which the detected light is minimum due to destructive interference?
In Fig. 35-37, two isotropic point sources S1 and S2 emit identical light waves in phase at wavelength . The sources lie at separation on an x axis, and a light detector is moved in a circle of large radius around the midpoint between them. It detects 30 points of zero intensity, including two on the x axis, one of them to the left of the sources and the other to the right of the sources. What is the value of ?
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