Chapter 9: Problem 9

An interference pattern is formed by sending red light through a pair of narrow slits. If blue light is then used, the spacing of the bright areas (where constructive interference takes place) won't be the same. How will it be different? Why?

Short Answer

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Answer: The spacing of the bright areas in an interference pattern decreases when switching from red light to blue light due to the shorter wavelength of blue light compared to red light. As a result, the bright areas become closer to each other when blue light is used.

Step by step solution

Understand the principles of interference pattern

An interference pattern is formed when light waves from two sources interfere with each other. The constructive interference, which is the bright areas in the pattern, occurs when the path difference between the waves is equal to an integer multiple of their wavelength.

Recall the formula for interference pattern

In a double-slit experiment, the position of the bright areas (constructive interference) is determined by the following formula: \(y = m \cdot \dfrac{\lambda L}{d}\) where: - \(y\) is the position of the bright area on a screen, - \(m\) is the order of interference (integer), - \(\lambda\) is the wavelength of the light, - \(L\) is the distance between the slits and the screen, - \(d\) is the distance between the slits.

Analyze the effect of changing the wavelength on the interference pattern

From the formula in Step 2, we see that the position of the bright areas (constructive interference) is directly proportional to the wavelength of the light (\(\lambda\)) used. When we switch from red light to blue light, we are effectively changing the wavelength of the light.

Compare the wavelengths of red and blue light

Red light has a longer wavelength (around 700 nm) than blue light (around 450 nm). Since the position of the bright areas is directly proportional to the wavelength, the change in the light will affect the interference pattern.

Determine the change in spacing of the bright areas

As we have established, the spacing is directly proportional to the wavelength of the light. When we switch from red light to blue light, the wavelength decreases. Therefore, the spacing of the bright areas (constructive interference) will also decrease. In other words, the bright areas will be closer to each other when we use blue light compared to when we use red light.

Conclusion

The spacing of the bright areas (constructive interference) in an interference pattern will be different when we switch from red light to blue light. The reason for this is that the position of these bright areas is directly proportional to the wavelength of the light. Since blue light has a shorter wavelength than red light, the spacing of the bright areas will be smaller, causing them to be closer to each other when blue light is used.

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An interference pattern is formed by sending red light through a pair of narrow slits. If blue light is then used, the spacing of the bright areas (where constructive interference takes place) won't be the same. How will it be different? Why?

Short Answer

Step by step solution

Understand the principles of interference pattern

Recall the formula for interference pattern

Analyze the effect of changing the wavelength on the interference pattern

Compare the wavelengths of red and blue light

Determine the change in spacing of the bright areas

Conclusion

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