A thin film of cooking oil (n=1.43) is spread on a puddle of water (n=1.34). What is the minimum thickness Dmin of the oil that will strongly reflect blue light having a wavelength in air of 451 nm, at normal incidence? Dmin= nm What are the next three thicknesses that will also strongly reflect blue light of the same wavelength, at normal incidence? 158 nm, 237 nm, and 315 nm 237 nm, 394 nm, and 552 nm 473 nm, 788 nm, and 1100 nm 361 nm, 602 nm, and 842 nm 315 nm, 473 nm, and 631 nm

Complete Question

A thin film of cooking oil (n=1.43) is spread on a puddle of water (n=1.34). What is the minimum thickness Dmin of the oil that will strongly reflect blue light having a wavelength in air of 451 nm, at normal incidence? Dmin= nm What are the next three thicknesses that will also strongly reflect blue light of the same wavelength, at normal incidence?

a)   158 nm, 237 nm, and 315 nm

b)   237 nm, 394 nm, and 552 nm

c)   473 nm, 788 nm, and 1100 nm

d)  361 nm, 602 nm, and 842 nm

e)  315 nm, 473 nm, and 631 nm

The minimum thickness is  

The correct option is B

Explanation:

  From the question we are told that

      The refractive index of cooking oil is

       The refractive index of water is

      The  wavelength of reflection is is  

The formula for the thickness of the oil film is mathematically represented as

Where n is the refractive index of oil

            m is the integer number of fringe

            t is the thickness

   for a minimum reflection  m= 0

Now making t the subject of the formula

Substituting value

For the next thickness m = 1

   so we have

For the next thickness m = 2

     so we have that  

For the next thickness m = 3

     so we have that

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