Suppose you have two monochromatic light beams. Beam has half the wavelength of beam \(2 .\) How do their frequencies compare? a. Beam 1 has 4 times the frequency of beam 2. b. Beam 1 has 2 times the frequency of beam 2. c. They are the same. d. Beam 1 has \(1 / 2\) the frequency of beam 2 e. Beam 1 has \(1 / 4\) the frequency of beam 2

Wavelength refers to the distance between two consecutive peaks (or troughs) of a light wave. It is typically represented by the Greek letter lambda (\( \lambda \)). Wavelengths of light are often measured in nanometers (nm) when dealing with visible light, since they are extremely small. The wavelength plays a crucial role in determining the color of visible light. For example, shorter wavelengths correspond to blue or violet light, while longer wavelengths correspond to red light.

Understanding wavelength is essential because it helps to determine other properties of light, such as frequency and energy. When dealing with different light beams, comparing their wavelengths can provide insights into their behavior and interaction with materials.

To illustrate, if the wavelength of beam 1 is half that of beam 2, as in the original exercise, this information can be used to explore how their frequencies compare, based on their wavelengths.

The speed of light (denoted as \( c \)) is a constant value representing how fast light travels through a vacuum. Its value is approximately \( 3 \times 10^8 \) meters per second (m/s). This speed is fundamental in physics and serves as a key constant in many equations and calculations.

Light's speed remains constant in a vacuum but may change when it passes through different mediums, such as air, water, or glass. However, the speed in a vacuum is what is most commonly referenced.

In the context of frequency and wavelength, the speed of light is used to establish their relationship. The equation \( c = u \lambda \) combines speed (\( c \)), frequency (\( u \)), and wavelength (\( \lambda \)). Using this equation, we can determine how changes in wavelength affect frequency, as seen in the original exercise.

The frequency-wavelength relationship is fundamental to understanding the behavior of light waves. Frequency (\( u \)) represents the number of wave cycles that pass a given point per second and is measured in hertz (Hz). The relationship between frequency and wavelength is inversely proportional. This means, as wavelength increases, frequency decreases, and vice versa.

This relationship is mathematically represented by the equation \( c = u \lambda \), where:\

• \( c \) is the speed of light
• \( u \) (nu) is the frequency
• \( \lambda \) (lambda) is the wavelength

From this equation, we can derive \( u = \frac{c}{\lambda} \). This shows that frequency can be calculated by dividing the speed of light by the wavelength.

In the original exercise, beam 1 has half the wavelength of beam 2. By using the given relationship, we can determine that beam 1 has twice the frequency of beam 2. This inverse proportionality helps us understand how changes in one property (wavelength) directly affect the other (frequency).