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Chapter 33: Q1P (page 1001)

A certain helium–neon laser emits red light in a narrow band of wavelengths centered at632.8nm and with a “wavelength width” (such as on the scale of Fig. 33-1) of0.0100nm. What is the corresponding “frequency width” for the emission?

Short Answer

Expert verified

The frequency width of the emission is7.49×109Hz

Step by step solution

01

Step 1: Listing the given quantities

Wavelength, λ=623.8nm=623.8×10-9m.

Wavelength width,Δλ=0.0100nm=0.0100×10-9m.

Speed of light, c=3×108m/s.

02

Step 2: Understanding the concepts of frequency and wavelength

In wavelength scale Fig. 33-1, each scale marker represents a change in wavelength and corresponding frequency. A certain scale denotes the electromagnetic spectrum. In this problem, we will calculate the frequency width of the He-Ne laser required for the emission using the formula for the change in frequency in terms of velocity of light and wavelength.

Formula:

Δf=Δcλ

03

Step 3: Calculations of the frequency width of the emission

Since Δλ≪λ, we will find Δfas,

Δf=Δcλ=cΔλλ2

Substitute the values in the above expression, and we get,

Δf=3×108623.8×10-9(0.0100×10-9)2=7.49×109Hz

The frequency width of the emission is7.49×109Hz.

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Most popular questions from this chapter

What is the wavelength of the electromagnetic wave emitted by the oscillator–antenna system of the following Fig. 33-3 ifL=0.253μHandC=25.0pF?

In Fig. 33-41, a beam of light, with intensity43 W/m2and polarization parallel to a y-axis, is sent into a system of two polarizing sheets with polarizing directions at angles of θ1=70°and θ2=90°to the y axis. What is the intensity of the light transmitted by the two-sheet system?

(a), unpolarized light is sent into a system of three polarizing sheets. The angles θ1,θ2 and θ3of the polarizing directions are measured counterclockwise from the positive direction of theyaxis (they are not drawn to scale).Angles θ1and θ3are fixed, but angleθ2 can be varied. Figure

(b) gives the intensity of the light emerging from sheet 3 as a function ofθ2 . (The scale of the intensity axis is not indicated.) What percentage of the light’s initial intensity is transmitted by the three-sheet system whenθ2=90° ?

Figure:

Each part of Fig. 33-34 shows light that refracts through an interface between two materials. The incident ray (shown gray in the figure) consists of red and blue light. The approximate index of refraction for visible light is indicated for each material. Which of the three parts show physically possible refraction? (Hint: First consider the refraction in general, regardless of the color, and then consider how red and blue light refract differently?

In Fig. 33-76, unpolarized light is sent into a system of three polarizing sheets with polarizing directions at angles, θ1=20°, θ2=60°andθ3=40°.What fraction of the initial light intensity emerges from the system?
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