Light of 633 nm wavelength is incident on two glass blocks, as shown below. Ther

Question

Light of 633 nm wavelength is incident on two glass blocks, as shown below. There is a curved
indentation in the top block, and the resulting gap between the two blocks is filled with water.
(a) How many bright fringes will be observed from above due to interference between light reflected
at the glass-water and water-glass interfaces?
(b) Suppose we gradually decrease the wavelength of the incident light, starting at 633 nm. What
is the first wavelength (in air) at which a bright fringe will appear exactly at x = 0.5 cm?

A diagram of the problem is here:
http://i38.tinypic.com/2556mp3.jpg Thank you ! http://i38.tinypic.com/2556mp3.jpg Thank you !

Explanation / Answer

wavelength L = 633 nm, n = 1.3, t = 0.8*10^-6 sin^2 (pi*x/w) m, w = 1 cm, (a) How many bright fringes will be observed from above due to interference between light reflected at the glass-water and water-glass interfaces? path difference = 2nt + L/2 = kL (k = 1, 2, ...) 2n*0.8*10^-6 sin^2 (pi*x/w) = (k - 1/2)L sin^2 (pi*x/w) = (k - 1/2)*0.304 sin (pi*x/w) = sqrt[(k - 1/2)*0.304] x = w/pi * sqrt[(k - 1/2)*0.304]

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