Calculating Red Light Frequency: A Physics Breakdown

Hey guys! Let's dive into a cool physics problem. We're gonna figure out the frequency of red light. This is super important because understanding light and its properties is key to lots of cool stuff, from how we see colors to how the internet works. So, grab your calculators and let's get started!

The Problem: Unpacking the Basics

Okay, so the problem gives us a few crucial pieces of information. First, we know that visible light, like all electromagnetic radiation, travels at a specific speed, which is approximately $3.0 \times 10^8 m/s$. This value is often represented by the letter c in physics equations. Next, we're told that the red light has a wavelength of $6.5 \times 10^{-7} m$. The wavelength is the distance between two consecutive crests or troughs of a wave. Finally, the question asks us to calculate the frequency of this red light. The frequency, usually denoted by the Greek letter nu (ν), tells us how many wave cycles pass a given point in one second. We're looking for the value of ν.

To solve this, we'll use a fundamental equation in physics that connects these three quantities: speed, wavelength, and frequency. This equation is pretty simple but incredibly powerful. Are you ready?

Understanding the Speed of Light

The speed of light is a constant, and it’s the fastest speed possible in the universe. It’s a fundamental physical constant. This speed is constant regardless of the source's motion. The speed of light is usually denoted as c and is approximately $3.0 \times 10^8 meters per second$. This value is incredibly important in many areas of physics. This constant is so important that it is a fundamental constant in the theory of special relativity, where it relates space and time. This means that the speed of light plays a role in how we perceive space and time.

The Role of Wavelength

Wavelength (λ) is the distance between identical points (adjacent crests) in the repeating wave. The wavelength is often measured in meters (m), or in nanometers (nm) which is $10^{-9}$ meters. The wavelength is inversely proportional to the frequency. This means that the higher the wavelength, the lower the frequency, and vice versa. It’s an essential property of waves, including light. This tells us a lot about the light. The color of light is determined by its wavelength, with red light having a longer wavelength than blue light. X-rays, for example, have a very short wavelength, which gives them the ability to penetrate matter, while radio waves have a very long wavelength.

Defining Frequency

Frequency (ν) is the number of waves that pass a fixed point in a given time, usually one second. It's measured in Hertz (Hz), where 1 Hz means one cycle per second. It is directly proportional to the energy of the wave. Frequency tells us how “rapidly” the wave oscillates. For light, the higher the frequency, the higher the energy. For example, ultraviolet light has a higher frequency than visible light, and is therefore more energetic. This is why UV exposure can cause sunburns.

The Physics Equation: Speed, Wavelength, and Frequency

The key to solving this problem lies in the following equation:

c = λ * ν

Where:

• c = speed of light ($3.0 \times 10^8 m/s$)
• λ = wavelength of the light (given as $6.5 \times 10^{-7} m$)
• ν = frequency of the light (what we want to find)

This equation tells us that the speed of light (c) is equal to the wavelength (λ) multiplied by the frequency (ν). It beautifully links these three properties of light.

Solving for Frequency: Let's Do the Math!

To find the frequency (ν), we need to rearrange the equation to solve for ν. We can do this by dividing both sides of the equation by the wavelength (λ):

ν = c / λ

Now we can plug in the values we know:

ν = ($3.0 \times 10^8 m/s$) / ($6.5 \times 10^{-7} m$)

When you work this out, the answer is:

ν ≈ $4.62 \times 10^{14} Hz$

So, the frequency of this red light is approximately $4.62 \times 10^{14} Hz$. None of the provided options (A, B, and C) matches this value. However, we can analyze the options to find out which is the closest.

Analyzing the Answers: Which One is the Closest?

Let’s analyze the provided options:

A. $2.2 \times 10^{-15} Hz$ B. $2.0 \times 10^2 Hz$

Neither of these options is close to our calculated value of approximately $4.62 \times 10^{14} Hz$. There seems to be an error in the provided options. The correct answer is not listed among the choices. If you had to pick the closest one, you would need more options to choose from.

The Importance of Units

It’s also important to make sure that the units are consistent throughout the calculation. The speed of light is given in meters per second (m/s), and the wavelength is given in meters (m). This ensures that the final answer for the frequency is in Hertz (Hz), which is cycles per second.

Conclusion: Light's Amazing Secrets

So there you have it! We've successfully calculated the frequency of red light using its wavelength and the speed of light. This exercise shows you how waves behave and how different properties of light are related. Remember, the relationship between speed, wavelength, and frequency applies not only to visible light but also to all types of electromagnetic radiation, including radio waves, microwaves, X-rays, and more. Understanding these concepts is fundamental to understanding the universe around us.

Keep exploring, and stay curious, guys! Physics can be a lot of fun!