5A. White light shines on a thin film of oil (n=1.6) sitting on top of water (n=

Question

5A. White light shines on a thin film of oil (n=1.6) sitting on top of water (n=1.33). Blue light (4700 A) is reflected. How thick is the oil? Please give at least three possible values. 5B. White light shines on a thin layer of water (n=1.33) sitting on top of crown glass (n=1.5) Green light (5500A) is reflected. How thick is the water? Please give at least three possible values. 5C. When there is a thin layer of oil on a flat surface, it is usually not one color but a rainbow of colors. What does this suggest about the layer of oil?

Explanation / Answer

here,

(a)

refractive index of oil , n1 = 1.6

refractive index of water , n2 = 1.33

wavelength , lamda = 4700 A

lamda = 4.7 * 10^-7 m

let the thickness of oil be t

wavelength = 2 * t * n1

4.7 * 10^-7 = 2 * t * 1.6

t = 1.47 * 10^-7 m

three possible values of thickness of oil is t , 2 * t , 3 * t

three possible values of thickness of oil is 1.47 * 10^-7 m , 2.93 * 10^-7 m, 4.41 * 10^-7 m

(b)

refractive index of crown glass , n1 = 1.5

refractive index of water , n2 = 1.33

wavelength , lamda = 5500 A

lamda = 5.5 * 10^-7 m

let the thickness of oil be t

wavelength = 2 * t * n2

5.5 * 10^-7 = 2 * t * 1.5

t = 1.83 * 10^-7 m

three possible values of thickness of water is t , 2 * t , 3 * t

three possible values of thickness of water is 1.83 * 10^-7 m , 3.66 * 10^-7 m, 5.49 * 10^-7 m

(c)

C) as there is a rainbow seen on the surface of oil which means different colors reflected from portions of oil layer ,

hence , the thickness of oil spill varies across it's area

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