Light of 600-nm wavelength interferes constructively when reflected from a soap bubble having...

Question:

Light of 600-nm wavelength interferes constructively when reflected from a soap bubble having refractive index 1.33. Determine the two lowest possible thicknesses of the soap bubble.

Light Interference:

Interference is defined as the phenomenon waves of the same frequency superimpose. This is portrayed when light passes through an interface such as a layer of thin films where reflected light rays either constructively interfere or destructively interfere with each other depending on their phase difference.

Answer and Explanation:

Here, constructive interference occurs when the following condition is satisfied:

{eq}\displaystyle t = \frac{ \left( m + \frac{1}{2} \right) \lambda}{2n} {/eq}


Here:

  • {eq}t {/eq} is the thickness of the soap bubble
  • {eq}m {/eq} is the order of reflection
  • {eq}\lambda {/eq} is the wavelength of light
  • {eq}n {/eq} is the index of refraction of the soap bubble


To determine the two lowest possible thickness of the soap bubble, we then consider solving this equation with {eq}m=0 {/eq} and {eq}m =1 {/eq}.

Hence, the two lowest possible thicknesses would be

{eq}\displaystyle t = \frac{ \left( 0 + \frac{1}{2} \right) 600\ \rm nm}{2(1.33)} \approx 112.8\ \rm nm {/eq}

{eq}\displaystyle t = \frac{ \left( 1 + \frac{1}{2} \right) 600\ \rm nm}{2(1.33)} \approx 338.3\ \rm nm {/eq}


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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