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A thin layer of liquid methylene iodide (n = 1.756) is sandwiched between two flat parallel...

Question:

A thin layer of liquid methylene iodide {eq}(n = 1.756) {/eq} is sandwiched between two flat parallel plates of glass {eq}(n = 1.50) {/eq}. What must be the thickness of the liquid layer if normally incident light with in air is to be strongly reflected?

Refractive Index:

A quantity that is used to measure the bending of any wave of light when it is moving from one medium to a different medium is known as the refractive index of that particular medium. It can be obtained by dividing the speed of light in a vacuum with the velocity of light in the medium.

Answer and Explanation:


Given data:

  • Refractive index of liquid methylene iodide, {eq}{n_l} = 1.756 {/eq}
  • Refractive index of glass, {eq}{n_g} = 1.50 {/eq}


For the light has to be strongly reflected then threshold be constructive interference, so from the condition of the constructive interference:

{eq}2{n_l}t = \left( {m + \dfrac{1}{2}} \right)\lambda {/eq}

For, minimum thickness

{eq}m = 0 {/eq}

Therefore,

{eq}\begin{align*} 2{n_l}t &= \dfrac{\lambda }{2}\\ t &= \dfrac{\lambda }{{4{n_l}}} \end{align*} {/eq}

Substitute the given values

{eq}\begin{align*} t &= \dfrac{\lambda }{{4 \times 1.765}}\\ t &= 0.1416\lambda \end{align*} {/eq}

Therefore, the thickness of the liquid layer is {eq}0.1416\lambda {/eq} .

Since, the value of wavelength {eq}\lambda {/eq} is not given in the problem. So we considered it as a variable.


Learn more about this topic:

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Constructive and Destructive Interference

from CLEP Natural Sciences: Study Guide & Test Prep

Chapter 8 / Lesson 16
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