For background on this problem, review Conceptual Example 4. Amixture of yellow

Question

For background on this problem, review Conceptual Example 4. Amixture of yellow light (wavelength = 574nm in vacuum) and violet light (wavelength = 419 nm in vacuum) falls perpendicular on a film ofgasoline that is floating on a puddle of water. For bothwavelengths the index of refraction of the gasoline is n =1.42 and that of water is n = 1.33. What is the minimum non-zero thickness of thefilm in a spot that looks (a) yellow and (b) violet because ofdestructive interference?

(a) thickness of film for yellow spot
1 nm

(b) thickness of film for violet spot
2 nm

Explanation / Answer

Here one region looks yellow because destructive interferencehas removed voilet light , while another region looks voiletbecause destructive interference has removed yellow light. the index of refraction for gasoline is ngasoline =1.42 for destructive interference here we have the conditionas 2ngasolinet =m for minimum non zero thickness m = 1 so t = /2ngasoline the thickness of film for yellow spot is tyellow = voilet /2ngasoline             = 419 nm / 2*1.42              = -------------- the thickness of film for violet spot is tvoilet = yellow /2ngasoline             = 574 nm / 2*1.42              = -------------- Hope this may help you . the thickness of film for yellow spot is tyellow = voilet /2ngasoline             = 419 nm / 2*1.42              = -------------- the thickness of film for violet spot is tvoilet = yellow /2ngasoline             = 574 nm / 2*1.42              = -------------- Hope this may help you .             = 574 nm / 2*1.42              = -------------- Hope this may help you .

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