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Chapter 35: Q9Q (page 1073)

Light travels along the length of a 1500 nm-long nanostructure. When a peak of the wave is at one end of the nanostructure, is there a peak or a valley at the other end of the wavelength (a) 500nm and (b) 1000nm?

Short Answer

Expert verified

(a)There is a 鈥榩eak鈥檃t the other end of the wave.

(b) There is a 鈥榲alley鈥� at the other end of the wave

Step by step solution

01

Given information

The total length of the nanostructure is, 1500nm.

The wavelength for case (a) is, 500nm.

The wavelength for case (b) is, 1000nm.

02

Wavelength

For a longitudinal wave, its wavelength can be defined as the distance between its two consecutive peaks or valleys.

The wavelength of any wave relies upon factors like wave frequency, wave propagation speed, and the propagating medium.

03

Step 3(a): The other end of the wave 

According to the question, the peak of the wave is at one end of the nanostructure, and also the wavelength is the distance between two peaks and valleys of a wave.

Then, the wave showing peak and valley can be drawn as,

Hence, there is a 鈥榩eak鈥� at the other end of the wave

04

Step 4(b): The other end of the wave 

Similarly, for a wavelength value of 1000nm, the wave having a peak at one end can be drawn as,

Hence, there is a 鈥榲alley鈥� at the other end of the wave.

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Most popular questions from this chapter

A disabled tanker leaks kerosene n=1.20into the Persian Gulf, creating a large slick on top of the watern=1.30). (a) If you are looking straight down from an airplane, while the Sun is overhead, at a region of the slick where its thickness is460nm, for which wavelength(s) of visible light is the reflection brightest because of constructive interference? (b) If you are scuba diving directly under this same region of the slick, for which wavelength(s) of visible light is the transmitted intensity strongest?

If mirror M2in a Michelson interferometer (fig 35-21) is moved through 0.233mm, a shift of 792 bright fringes occurs. What is the wavelength of the light producing the fringe pattern?

Figure 35-29 shows the transmission of light through a thin film in the air by a perpendicular beam (tilted in the figure for clarity). (a) Did rayr3undergo a phase shift due to reflection? (b) In wavelengths, what is the reflection phase shift for rayr4? (c) If the film thickness is L, what is the path length difference between raysr3andr4?

Figure 35-27a shows the cross-section of a vertical thin film whose width increases downward because gravitation causes slumping. Figure 35-27b is a face-on view of the film, showing four bright (red) interference fringes that result when the film is illuminated with a perpendicular beam of red light. Points in the cross section corresponding to the bright fringes are labeled. In terms of the wavelength of the light inside the film, what is the difference in film thickness between (a) points a and b and (b) points b and d?

Transmission through thin layers. In Fig. 35-43, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4(the light reflects twice inside material 2). The waves of r3 and r4 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min). For this situation, each problem in Table 35-3 refers to the indexes of refraction n1,n2andn3, the type.

Of interference, the thin-layer thickness L in nanometres, and the wavelength 位 in nanometres of the light as measured in air.

Where 位 is missing, give the wavelength that is in the visible range.

Where Lis missing, give the second least thickness or the third least thickness as indicated?
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