Ch 17: Superposition

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 17: Superposition

문제 13

17장, 문제 13

A carbon dioxide laser is an infrared laser. A CO₂ laser with a cavity length of 53.00 cm oscillates in the m=100,000 mode. What are the wavelength and frequency of the laser beam?

검증된 단계별 안내

The wavelength of the laser beam can be determined using the relationship between the cavity length and the mode number. For a standing wave in a laser cavity, the wavelength is given by:

λ = \frac{2}{m} L

, where

L

is the cavity length and

m

is the mode number.

Substitute the given values into the formula:

λ = \frac{2}{100,000} (53.00)

cm. Ensure the cavity length is in meters for consistency in SI units.

To find the frequency of the laser beam, use the relationship between the speed of light, wavelength, and frequency:

c = λ f

, where

c

is the speed of light (approximately

3.00 \times 10^8

m/s),

λ

is the wavelength, and

f

is the frequency.

Rearrange the formula to solve for frequency:

f = \frac{c}{λ}

. Substitute the calculated wavelength and the speed of light into this equation.

Perform the calculations to determine the wavelength in meters and the frequency in hertz. Ensure all units are consistent throughout the process.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Laser Operation

Lasers operate on the principle of stimulated emission, where an excited atom or molecule releases a photon of light, which then stimulates other excited atoms to emit more photons. This process creates a coherent beam of light, characterized by its monochromaticity and directionality. In the case of a CO2 laser, the specific gas mixture and cavity design determine the wavelength and frequency of the emitted light.

Wavelength and Frequency Relationship

Wavelength and frequency are inversely related properties of electromagnetic waves, described by the equation c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency. This relationship indicates that as the wavelength increases, the frequency decreases, and vice versa. Understanding this relationship is crucial for calculating the wavelength and frequency of the laser beam based on its mode of oscillation.

Mode of Oscillation

The mode of oscillation in a laser refers to the specific standing wave patterns that can form within the laser cavity. Each mode is characterized by a quantum number, which in this case is m=100,000 for the CO2 laser. The mode number helps determine the wavelength of the emitted light, as it relates to the length of the cavity and the number of wavelengths that fit within it, influencing the laser's output characteristics.