Question

Blue light of wavelength 480nm is most strongly reflected off a thin film of oil on a glass slab when viewed near normal incidence. Assuming that the index of refraction of the oil is 1.2 and that of the glass is 1.6. What is the minimum thickness of the oil film (other than zero)?
(A) 100nm
(B) 200nm
(C) 300nm
(D) None

Answer 1

The two reflections that cause interference are from the air oil interface and the oil glass interface. We can solve it by using the wavelength and thickness formula.

Formula used: The formula used here, would be:
${\text{t = }}\dfrac{\lambda }{{\text{2}}}$
Here, ${\text{t}}$ is the thickness.
$\lambda$ is the wavelength.

Complete step by step answer:
Let us assume that, initially the blue light falls and it has a wavelength of 480nm.
Refractive index of oil is 1.2
And, refractive index of glass is 1.6
At the interface, in both cases the electric field reflected is shifted ${\text{18}}{{\text{0}}^{\text{0}}}$, so to have a strong reflection they are already in phase. A thickness of zero would give a strong reflection; the next possibility is a thickness such that the extra path covered by the second reflection is one wavelength longer.
Applying the formula,
${\text{t = }}\dfrac{\lambda }{{\text{2}}}$
${\text{t = }}\dfrac{{{\lambda _{{\text{oil}}}}}}{{\text{2}}}{\text{ = }}\dfrac{{{\lambda _{{\text{air}}}}}}{{{\text{2}}{{\text{n}}_{{\text{oil}}}}}}{\text{ = }}\dfrac{{{\text{480}}}}{{{\text{2}}.{\text{4}}}}{\text{ = 200nm}}$
So, now we select the appropriate option.
Hence, the correct option is B.

** Note**
Refraction is the bending of light (it also happens with sound, water and other waves) as it passes from one transparent substance into another. This bending by refraction makes it possible for us to have lenses, magnifying glasses, prisms and rainbows. And also, our eyes depend upon this bending of light. The change in speed that occurs when light passes from one medium to another is responsible for the bending of light, or refraction, that takes place at an interface. If light is travelling from medium 1 into medium 2, and angles are measured from the normal to the interface, the angle of transmission of the light into the second medium is related to the angle of incidence by Snell's law. Some day-to-day life examples of refraction is a bending of the sun's rays as they enter raindrops, forming a rainbow. Another example of refraction is a prism.