In order to decide the thickness of a SiO2 layer(n=1.5) on Si, a wedge is prepared as shown in the picture. A total of 7 DARK fringes was observed, when light of wavelength 589nm shines prependicularly on the wedge. It is known that light reflected from the Si/SiO2 surface would have a phase change of π rad.
( I don't know why the image cannot appear after posting, it does appear in edit mode. Here is the link:
i) Determine whether the fringe at the thinner end of the SiO2 wedge is bright or dark. Explain briefly. (2M)
ii) Calculate the thickness of the SiO2 layer. (3M)
iii) If the setup is illuminated by a light of shorter wavelength, what chages would you expect for the number of fringes observed? Explain briefly. (2M)
iv) If the setup is placed in water(n=1.33), what changes would you expect for the number of fringes observed? Explain your answer briefly. (2M)
For constructive interference, 2nt = (m+1/2)λ, m = 0, 1, 2......
For destructive interference, 2nt = mλ, m = 0, 1, 2......
The Attempt at a Solution
i) Dark? Just guess. What should I consider?
ii) 2nt = mλ, m = 7
2(1.5)t = 7*(589*10^-9)
t = 1.96*10^-7m
iii) Just guess: Because 2nt = mλ, where 2nt is a constant. When λ decreases, m has to be increased. So the number of fringes observed increases.
iv) Same? But it doesn't seem correct......