Im really struggling with this problem can anyone help? Thanks For background on

Question

Im really struggling with this problem can anyone help? Thanks
For background on this problem, review Conceptual Example 4. Amixture of yellow light (wavelength = 589nm in vacuum) and violet light (wavelength = 416 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 =1.40 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


(b) thickness of film for violet spot

Im really struggling with this problem can anyone help? Thanks
For background on this problem, review Conceptual Example 4. Amixture of yellow light (wavelength = 589nm in vacuum) and violet light (wavelength = 416 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 =1.40 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?

Explanation / Answer

wavelength of yellow = 589 nm = 589 * 10 ^ -9m wavelength of violet ' = 416 nm = 416 * 10 ^ -9m index of refraction of gasoline n = 1.4 (a). minimum thickness of film to appear yellow spot t = / 4n                                                                                  = 105.17 nm (b). minimum thickness of film to appear violet spoy t '= ' / 4n                                                                                   = 74.28 nm

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