# 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.

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} 