A thin film of plastic of thickness d = 1 times 106 m coats a flat piece of glas

Question

A thin film of plastic of thickness d = 1 times 106 m coats a flat piece of glass. The index of refraction of the plastic and glass are n_p = 1.25 and n_g = 1 .50, respectively. White light impinges on the plastic from the air at near-normal incidence. Recall that the visible spectrum extends from wavelengths of 400 nm to 700 nm. For what longest wavelength of visible light will there be constructive interference in the reflected light? 5.40 times 10^-7 6.53 times 10^-7 6.25 times 10^-7 5.85 times 10^-7 For what shortest wavelength of visible light will there be destructive interference? 4.55 times 10^-7 4.25 times 10^-7 4.8x10^-7 4.36 times 10^-7 How long (in s) does it take a photon to make a round trip through the plastic coating? Neglect any time-delay at the plastic-glass interface. 7.20 times 10^-15 6.53 times 10^-15 8.33 times 10^-15 7.80 times 10^-15

Explanation / Answer

A) For constructive interference

   => 2nd = m * lambda

=> 2 * 1.25 * 1 * 10-6 = 4 * lambda

=>    lambda =   6.25 * 10-7 m

=>    longest wavelength of visible light = 6.25 * 10-7 m

B)    For destructive interference

   => 2nd = (2m + 1)/2 * lambda

=> 4 * 1.25 * 1 * 10-6 = 11 * lambda

=>    lambda =   4.55 * 10-7 m

=>    shortest wavelength of visible light = 4.55 * 10-7 m

C)    Time taken = (2 * 10-6 * 1.25)/(3 * 108)

                           =   8.33 * 10-15 sec

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