Yellow Light Has A Frequency Of $5.2 \times 10^{14} , \text{Hz}$ And Travels At A Speed Of $3.0 \times 10^8 , \text{m/s}$. What Is The Wavelength Of Yellow Light, In Meters?A. 5.8 × 10 − 7 M 5.8 \times 10^{-7} \, \text{m} 5.8 × 1 0 − 7 M B.

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Introduction

In the realm of physics, light is a form of electromagnetic radiation that exhibits both wave-like and particle-like properties. One of the fundamental characteristics of light is its frequency, which is a measure of the number of oscillations or cycles per second. The frequency of light is typically denoted by the symbol ν (nu) and is measured in units of hertz (Hz). Another important property of light is its wavelength, which is a measure of the distance between two consecutive peaks or troughs of a light wave. In this article, we will explore the relationship between the frequency and wavelength of light, and use this knowledge to calculate the wavelength of yellow light.

The Speed of Light and Its Relationship to Frequency and Wavelength

The speed of light in a vacuum is a fundamental constant of the universe, denoted by the symbol c and measured to be approximately 3.0 x 10^8 meters per second (m/s). The speed of light is related to its frequency and wavelength by the following equation:

c = λν

where c is the speed of light, λ (lambda) is the wavelength of light, and ν (nu) is the frequency of light.

Calculating the Wavelength of Yellow Light

Given the frequency of yellow light as 5.2 x 10^14 Hz and its speed as 3.0 x 10^8 m/s, we can use the equation above to calculate its wavelength. Rearranging the equation to solve for λ, we get:

λ = c / ν

Substituting the given values, we get:

λ = (3.0 x 10^8 m/s) / (5.2 x 10^14 Hz)

To perform this calculation, we need to divide the numerator by the denominator, which involves multiplying the numerator by the reciprocal of the denominator. This gives us:

λ = (3.0 x 10^8 m/s) x (1 / (5.2 x 10^14 Hz))

Using the rule for dividing numbers with exponents, we can rewrite this as:

λ = (3.0 x 10^8 m/s) x (1 x 10^(-14) Hz^(-1))

Now, we can simplify this expression by multiplying the numbers and adding the exponents:

λ = 3.0 x 10^(-6) m

Therefore, the wavelength of yellow light is approximately 3.0 x 10^(-6) meters.

Conclusion

In conclusion, we have used the equation c = λν to calculate the wavelength of yellow light, given its frequency and speed. By rearranging the equation to solve for λ, we were able to substitute the given values and perform the necessary calculations to obtain the wavelength of yellow light. This calculation demonstrates the relationship between the frequency and wavelength of light, and highlights the importance of understanding this relationship in the study of physics.

Discussion

The calculation of the wavelength of yellow light is a simple application of the equation c = λν. However, this equation has far-reaching implications in the study of physics, particularly in the fields of electromagnetism and optics. The speed of light is a fundamental constant of the universe, and its relationship to frequency and wavelength is a key concept in understanding the behavior of light.

References

  • [1] Halliday, D., Resnick, R., & Walker, J. (2013). Fundamentals of physics. John Wiley & Sons.
  • [2] Serway, R. A., & Jewett, J. W. (2018). Physics for scientists and engineers. Cengage Learning.

Additional Resources

Frequently Asked Questions

  • Q: What is the relationship between the frequency and wavelength of light? A: The frequency and wavelength of light are related by the equation c = λν, where c is the speed of light, λ is the wavelength of light, and ν is the frequency of light.
  • Q: How do I calculate the wavelength of light given its frequency and speed? A: To calculate the wavelength of light, you can use the equation λ = c / ν, where c is the speed of light and ν is the frequency of light.
  • Q: What is the wavelength of yellow light? A: The wavelength of yellow light is approximately 3.0 x 10^(-6) meters.
    Frequently Asked Questions About the Wavelength of Light ===========================================================

Q: What is the relationship between the frequency and wavelength of light?

A: The frequency and wavelength of light are related by the equation c = λν, where c is the speed of light, λ is the wavelength of light, and ν is the frequency of light. This equation shows that the speed of light is equal to the product of its wavelength and frequency.

Q: How do I calculate the wavelength of light given its frequency and speed?

A: To calculate the wavelength of light, you can use the equation λ = c / ν, where c is the speed of light and ν is the frequency of light. This equation shows that the wavelength of light is equal to the speed of light divided by its frequency.

Q: What is the wavelength of yellow light?

A: The wavelength of yellow light is approximately 3.0 x 10^(-6) meters. This value is based on the frequency of yellow light, which is 5.2 x 10^14 Hz, and the speed of light, which is 3.0 x 10^8 m/s.

Q: How does the wavelength of light affect its behavior?

A: The wavelength of light affects its behavior in several ways. For example, the wavelength of light determines its ability to pass through different materials, such as glass or water. It also affects the way light interacts with matter, such as the way it scatters or absorbs.

Q: What are some common applications of the wavelength of light?

A: The wavelength of light has many practical applications in fields such as medicine, telecommunications, and materials science. For example, the wavelength of light is used in medical imaging techniques such as optical coherence tomography (OCT) to create high-resolution images of the retina. It is also used in telecommunications to transmit data through fiber optic cables.

Q: Can the wavelength of light be changed?

A: Yes, the wavelength of light can be changed through various techniques such as refraction, diffraction, and interference. For example, a prism can be used to refract light and change its wavelength, while a diffraction grating can be used to diffract light and change its wavelength.

Q: What are some common sources of light with different wavelengths?

A: There are many common sources of light with different wavelengths, including:

  • Incandescent bulbs, which emit light with a wavelength of around 600-800 nanometers (nm)
  • Fluorescent bulbs, which emit light with a wavelength of around 400-500 nm
  • LEDs, which emit light with a wavelength of around 400-700 nm
  • Lasers, which emit light with a wavelength of around 400-1000 nm

Q: How does the wavelength of light affect its color?

A: The wavelength of light affects its color in a way that is determined by the way our eyes perceive different wavelengths of light. For example, light with a wavelength of around 400-500 nm is perceived as blue, while light with a wavelength of around 600-800 nm is perceived as red.

Q: Can the wavelength of light be used to measure distance?

A: Yes, the wavelength of light can be used to measure distance through a technique called interferometry. This technique involves splitting light into two beams and then recombining them to create an interference pattern, which can be used to measure the distance between two points.

Q: What are some common applications of interferometry?

A: Interferometry has many practical applications in fields such as astronomy, materials science, and engineering. For example, it is used in the study of the structure of the universe, the properties of materials, and the behavior of complex systems.

Q: Can the wavelength of light be used to measure temperature?

A: Yes, the wavelength of light can be used to measure temperature through a technique called pyrometry. This technique involves measuring the wavelength of light emitted by an object and using it to calculate its temperature.

Q: What are some common applications of pyrometry?

A: Pyrometry has many practical applications in fields such as materials science, engineering, and medicine. For example, it is used in the study of the properties of materials, the behavior of complex systems, and the diagnosis of medical conditions.