Which of the following equations should be used to find the minimum thickness t of the oil film that satisfies the conditions of the problem? let λ be the wavelength of light in air and n the index of refraction of the thin filma. 2t=mλn(m=0,1, for constructive interference. b.2t=(m+12)λn(m=0,1, for destructive interference. c.2t=(m+12)λn(m=0,1, for constructive interference. d. 2t=mλn(m=0,1, for destructive interference.

The equations are:

C. 2t=(m+12)λn(m=0,1,2,...) for constructive interference. (Here is a mistake in this equation i.e. m + 12 (wrong) and m + 1/2 (correct)). So, the correct equation for constructive interference is:

2t = (m + 1/2) λ n (m=0,1,2,...)  

D. 2t=mλn(m=0,1,2,...) for destructive interference.

Explanation:

Constructive Interference occurs when two waves’ crests or troughs add together therefore, the resulting wave amplitude is equal to the sum of the each wave amplitude (in this case the amplitude of each wave is of same charge).

Destructive Interference occurs when a waves’ crest and trough cancel each other therefore, the resulting wave amplitude is zero (in this case the amplitude of each wave is oppositely charged).

When the refractive index of the medium in which the light travels is lower than the refractive index of the thin film medium then a 180° phase shift occurs.

When the light wave strikes the top surface of thin film, the wave reflects from the top surface and the reflecting light wave shifts by half of wavelength i.e. λ/2

When the light wave strikes the bottom surface of thin film then the light wave does not shift however, the light cover extra distance (2t), reflecting from the bottom surface to travel back to air.

Since, oil has refractive index (n = 1.5) which is higher than the refractive index of air (n = 1) so, when light wave strikes on the top surface of thin film of oil, the reflecting wave will shift by λ/2 (because nair < noil) and when light wave strikes on the bottom surface of thin film of oil, it will cover an extra distance to travel back to air and no wavelength shift will occur (because noil > nair).

In light of the above situation, the constructive interference of light reflected from the thin oil film is:

2t = (m + 1/2) λ n  

The destructive interference of light reflected from the thin film is:  

2t = m λ n

b.

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