contestada

A 360 nm thick oil film floats on the surface of a pool of water. The indices of refraction of the oil and water at 1.50 and 1.33 respectively. When the surface of the oil is illuminated from above at normal incidence with white light, what is the wavelength of light between 400 nm to 800 nm wavelength that is most weakly reflected?

Respuesta :

Answer:

[tex]\lambda_{oil} = 540\ nm[/tex]

Explanation:

given,

thickness of oil, t = 360 nm

refractive index of oil = 1.50

refractive index of water = 1.33

range of wavelength = 400 nm to 800 nm

In the case of destructive interference

   [tex]2 n_{oil} d = m \lambda_{oil}[/tex]

for m = 1

  [tex]\lambda_{oil} = \dfrac{2 n_{oil} d}{m}[/tex]

  [tex]\lambda_{oil} = \dfrac{2\times 1.5 \times 360}{1}[/tex]

  [tex]\lambda_{oil} = 1080\ nm[/tex]

not in the range

now, for m = 2

  [tex]\lambda_{oil} = \dfrac{2 n_{oil} d}{m}[/tex]

  [tex]\lambda_{oil} = \dfrac{2\times 1.5 \times 360}{2}[/tex]

  [tex]\lambda_{oil} = 540\ nm[/tex]

hence, the wavelength of light which is  most weakly reflected is 540 nm.