Question

a. Which has a longer wavelength: green light or yellow light? b. Which has a higher frequency: an X ray or a microwave? c. Which travels at a greater speed: ultraviolet light or infrared light?

Short answer

a. Yellow light has a longer wavelength than green light. b. An X-ray has a higher frequency than a microwave. c. Ultraviolet light and infrared light travel at the same speed.

Step-by-step solution

Understanding Wavelength and Color

Wavelengths of visible light correspond to different colors. In general, green light has a wavelength of approximately 495-570 nm, while yellow light has a wavelength of approximately 570-590 nm. Since a longer wavelength indicates a larger numerical value, yellow light has a longer wavelength than green light.

Understanding Frequency

Frequency and wavelength are inversely related through the equation \( c = \lambda \u \), where \( c \) is the speed of light, \( \lambda \) is the wavelength, and \( \u \) is the frequency. X-rays have much shorter wavelengths compared to microwaves, meaning they have higher frequencies.

Comparing the Speed of Different Types of Light

All electromagnetic waves, including ultraviolet light and infrared light, travel at the same speed in a vacuum, which is the speed of light \( (c \approx 3 \times 10^{8} \text{m/s}) \). Thus, ultraviolet light and infrared light travel at the same speed.

Key concepts

Wavelength

Wavelength is the distance between two consecutive peaks or troughs in a wave. It is usually measured in nanometers (nm) for visible light. Different colors of light have different wavelengths. For example, green light has a wavelength of approximately 495-570 nm, while yellow light has a wavelength of 570-590 nm. Therefore, yellow light has a longer wavelength than green light. Remember, Wavelengths are inversely proportional to frequency: as one increases, the other decreases.

Frequency

Frequency refers to the number of wave cycles that pass a fixed point per unit of time, usually measured in Hertz (Hz). Frequency and wavelength are inversely related through the equation: c = λu where: - c is the speed of light ( approximately 3 x 10^8 m/s), - λ (lambda) is the wavelength, - u (nu) is the frequency. This means that waves with shorter wavelengths have higher frequencies. For instance, X-rays have much shorter wavelengths and thus higher frequencies compared to microwaves.

Speed of Light

The speed of light is a constant in a vacuum: approximately 3 x 10^8 meters per second (m/s). This constant speed applies to all forms of electromagnetic radiation, whether it’s visible light, ultraviolet light, or infrared light. However, when electromagnetic waves pass through different media (like air, water, or glass), their speed can change slightly. Despite these variations, the speed of light in a vacuum remains the universal speed limit for all forms of electromagnetic energy.

Visible Light

Visible light is the portion of the electromagnetic spectrum that is visible to the human eye, typically ranging from 380 nm to 750 nm in wavelength. It includes all the colors that we can see, from violet through red. Each color corresponds to a specific range of wavelengths:

• Violet: 380-450 nm
• Blue: 450-495 nm
• Green: 495-570 nm
• Yellow: 570-590 nm
• Orange: 590-620 nm
• Red: 620-750 nm

Understanding the wavelengths of different colors helps in comprehending why some colors, like yellow, have longer wavelengths than others, such as green.

Electromagnetic Waves

Electromagnetic waves are waves of electric and magnetic fields that propagate through space. They include a diverse range of wave types, from long-wavelength radio waves to short-wavelength gamma rays. All electromagnetic waves travel at the speed of light in a vacuum. The electromagnetic spectrum is divided into different regions based on wavelength and frequency, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Each type has unique properties and uses:

• Radio Waves: Used in communication (e.g., radio, television)
• Microwaves: Used in cooking and radar
• Infrared: Experienced as heat and used in remote controls
• Visible Light: The only part of the spectrum visible to the human eye
• Ultraviolet: Used in sterilization and detecting forged banknotes
• X-rays: Used in medical imaging
• Gamma Rays: Used in cancer treatment and emitted by radioactive substances

These waves are fundamental in various technologies, each relying on specific wavelengths and frequencies.