Focus: Understanding frequency, wavelength, and their relationship to the speed of light.
Goal: Comprehend why the speed of light ( c) is equal to wavelength ( ) times frequency ( ).
Highlight the beauty of mathematics in describing nature.
Frequency (ν): Symbolized by the Greek letter nu.
Definition: The number of wave cycles passing a point per second.
A wave cycle: One complete up/down motion.
Wavelength (λ): Represented by the Greek letter lambda.
Definition: Distance between two consecutive wave cycles.
Inverse relationship: Longer wavelength = lower frequency
Shorter wavelength = higher frequency.
Measurement of frequency: Expressed in cycles per second (s⁻¹) or Hertz (Hz).
Speed of light (c): 3 x 10⁸ m/s or 300 million m/s.
Example: Signal from Earth to a friend 300 million meters away takes 1 second.
More realistic example: Light from the Moon takes 1.23 seconds to reach Earth, reflecting past events on the Moon.
Scientific notation: Speed of light is often expressed as 3 x 10⁸ m/s.
This remarkable speed is consistent across different types of light waves, from visible light to radio waves, which all travel at the same speed.
Visible light range: 400 - 700 nanometers.
Types of light waves: Radio waves, microwaves, infrared, ultraviolet, X-rays, gamma rays.
Importance: All move at the speed of light (3 x 10⁸ m/s).
Relationship formula:
Speed of light (c) = Wavelength (λ) x Frequency (ν)
Calculation examples:
Wavelength of 1 meter → frequency of 3 x 10⁸ Hz.
Wavelength of 2 meters → frequency of 1.5 x 10⁸ Hz.
Wavelength of 0.5 meters → frequency of 6 x 10⁸ Hz.
Inverse relationship between wavelength and frequency:
As wavelength decreases, frequency increases proportionally.
This relationship holds true due to the constancy of the speed of light.
Conclusion: The equation λν = c describes a fundamental characteristic of light.
Mathematics provides insight into natural phenomena, exemplified by the relationship described between frequency, wavelength, and the speed of light.
An interesting thought: Light from the sun takes about 8 minutes and 19 seconds to reach Earth, emphasizing the vastness of space and the speed at which light travels.
Characteristics of Light Waves