Question

The thickness of a layer of benzene ( n = 1.50 ) floating on water by shining monochromatic light onto the film and varying the wavelength of the light. The wavelength of 575 nm is reflected the most strongly from the film. What is the minimum thickness of the film? What wavelength of light is reflected the least at this thickness? Is this wavelength in the visible spectrum? step by step please include all derived equations.

Answer 1

for oil film where refractive index of oil is higher than the refractive index of water,

for constructive interference,

2*n_oil*d*cos(theta)=(m-0.5)*lambda

where n_oil=refractive index of oil

d=thickness of oil film

theta=angle of incidence

m=order of the interference

lambda=wavelength

for destructive interference:

2*n_oil*d*cos(theta)=m*lambda

part a:

given lambda=575 nm

n_oil=1.5

theta=0 degrees

for minimum thickness, m=1

then using the formula for constructive interference,

2*1.5*d*cos(0)=0.5*575 nm

==>d=95.833 nm

part b:

let wavelength of lambda is reflected the least at this thickness.

using the formula for destructive interference with m=1:

2*1.5*d*cos(0)=1*lambda

==> lambda=287.5 nm

part c:

this wavelength is not in visible spectrum as visible spectrum lies in the range of 390 nm-700 nm