What visible wavelengths of light are strongly reflected from a …

Physics Questions
Short Answer
Step by Step Solution
Physics Questions

A soap bubble is essentially a thin film of water surrounded by air. the colors you see in soap bubbles are produced by interference. part a what visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

Short Answer

The colors in a bubble arise from the interference of waves reflecting off its surface and inside it. Constructive interference occurs when the phase difference between these waves is an integer multiple of 2≈ìA, which can be calculated using the bubble’s thickness, leading to observable colors such as violet and red based on specific wavelengths.

Step-by-Step Solution

Step 1: Understanding Bubble Colors Through Interference

The colors seen in a bubble result from the interference of two waves. These waves are:

  • The wave reflected off the bubble’s surface.
  • The wave that travels inside the bubble and reflects off the back.
This interference leads to differences in color depending on the wave phases.

Step 2: Phase Condition for Constructive Interference

For the waves to constructively interfere, the phase difference between them needs to be an integer multiple of 2œA. The phase difference can be calculated using the equation:

  • ≈íi≈ìU = k≈íix – ≈ìA
Here, ≈íix is double the bubble’s thickness, accounting for the wave’s travel path. To achieve constructive interference, we set the equation to equal 2m≈ìA, where m is any integer.

Step 3: Calculating Wavelengths and Observing Colors

By substituting the values into the derived formula, we can determine the wavelengths in air. The equation for the wavelength is:

  • ≈í¬™’ = 2nt / (m + 1/2)
Using a bubble thickness (t) of 390 nm and varying m yields wavelengths of 415 nm (violet) and 692 nm (red), resulting in the observable colors of red and violet in the bubble.

Related Concepts

Interference

The phenomenon that occurs when two waves overlap and combine, affecting the resultant amplitude and color observed depending on their phase relationship.

Constructive Interference

A type of wave interference where waves combine in such a way that their amplitudes add together, resulting in a brighter or intensified signal, conditionally occurring when the phase difference is an integer multiple of 2œa.

Wavelength

The distance between successive peaks of a wave, which determines the color perceived in visible light, characterized by specific values that correlate with different colors in the light spectrum.

Table Of Contents
  1. A soap bubble is essentially a thin film of water surrounded by air. the colors you see in soap bubbles are produced by interference. part a what visible wavelengths of light are strongly reflected from a 390-nm-thick soap bubble?

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