Chapter 9: Problem 8

If the wavelength of visible light were around $10 \mathrm{~cm}$ instead of 500 $\mathrm{nm}$ and we could still see it, what effect would this have on our ability to see diffraction and interference effects?

Short Answer

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Answer: Changing the wavelength of visible light from 500 nm to 10 cm results in diffraction and interference patterns becoming significantly larger and wider. This makes these patterns more noticeable and easier to observe. However, the level of detail in the visible range would likely be decreased due to the larger wavelengths, reducing the resolving power of our eyes. While diffraction and interference patterns would be more apparent, the overall quality of the images we see might be reduced.

Step by step solution

Understand the key concepts of diffraction and interference

Diffraction is the bending of light waves around small obstacles and the spreading of light waves through small openings. The extent of diffraction depends on the size of the obstacle/opening and the wavelength of the light. When light waves overlap, they can combine constructively or destructively, resulting in an interference pattern. The ability to see interference patterns depends on the distance between different maxima or minima on the screen or surface.

Calculate the ratio of the new wavelength to the old wavelength

Given, the old wavelength of visible light is 500 nm, and the new wavelength is 10 cm. To compare the two, convert them into the same units. Recall that 1 m = 100 cm and 1 m = 1x10^9 nm. The new wavelength is 10 cm = 0.1 m, and the old wavelength is 500 nm = 5x10^-7 m. The ratio of the new wavelength to the old wavelength is: $$\frac{\lambda_{new}}{\lambda_{old}} = \frac{0.1}{5 \times 10^{-7}} = 2 \times 10^{7}$$

Analyze the effect on diffraction and interference patterns

With the new wavelength being 2x10^7 times larger than the old wavelength, the diffraction and interference patterns will be significantly larger, resulting in wider patterns. This can be seen in Young's double-slit experiment equation: $$y = \frac{L\lambda}{d}$$ Where $y$ is the fringe separation, $L$ is the distance between the double-slit and the screen, $\lambda$ is the wavelength of the light, and $d$ is the distance between the slits. As the wavelength increases, the value of $y$ will also increase.

Analyze the effect on our ability to see diffraction and interference patterns

The increase in the size of the diffraction and interference patterns will make those effects much more noticeable and easier to observe. However, the level of detail available in the visible range would likely be decreased due to the larger wavelengths, reducing the resolving power of our eyes. So, while diffraction and interference patterns would be more apparent and easier to spot, the overall quality of the images we see might be reduced.

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If the wavelength of visible light were around \(10 \mathrm{~cm}\) instead of 500 \(\mathrm{nm}\) and we could still see it, what effect would this have on our ability to see diffraction and interference effects?

Short Answer

Step by step solution

Understand the key concepts of diffraction and interference

Calculate the ratio of the new wavelength to the old wavelength

Analyze the effect on diffraction and interference patterns

Analyze the effect on our ability to see diffraction and interference patterns

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