# Physics Tutorial: Electromagnetic Waves. Light

In this Physics tutorial, you will learn:

• What are electromagnetic waves?
• How are produced the EM waves?
• What is the propagation speed of EM waves?
• What is the electromagnetic spectrum?
• How do we classify the EM waves?
• How are the EM waves used in technology?
• Which kind of EM waves should we avoid?
• What are the penetrating abilities of EM waves?
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11.6Electromagnetic Waves. Light

## Introduction to Electromagnetic Waves. Light

Why do doctors advise aganst extended periods in direct sunlight in summer days?

Why you can get burned when staying close to a heat source even when you are not touching it?

How it is possible that sun energy comes to us through empty space?

Do you think the energy produced by the Sun is composed only by light energy? Why?

All these questions (and many others) will get answer in this tutorial, when electromagnetic waves will be discussed in details. The topic of EM waves is crucial in understanding the waves behaviour and many related phenomena we encounter in everyday life.

## What Are Electromagnetic Waves?

Electromagnetic (in short EM) waves are transverse waves emitted by hot objects when they release some of their energy to the surroundings during the cooling process. These waves have different frequencies, depending on their temperature. We will see in Section 13 that internal energy of objects is proportional to their temperature. The entirety of EM waves produced by a hot source is otherwise known as Electromagnetic Radiation. Sun is our main source of EM radiation. Since the Sun is about 150 million kilometres away from the Earth, most of the path followed by EM waves that fall on the Earth consists on vacuum. Therefore, EM waves propagate differently from mechanical ones, i.e. unlike mechanical waves, EM waves do not need a material medium to propagate as discussed in our Physics tutorial on "Types of Waves and the Simplified Equation of Waves"

EM waves propagate at a very high speed. In vacuum the speed of EM waves reach a value of 300 000 km/s. This is the highest known speed in the universe. Since the speed of EM waves is much greater than the other known speeds, we use the letter 'c' instead of 'v' to represent it in formulae. Thus, the equation of waves for EM radiation becomes

c = λ × f

where λ is the wavelength and f is the frequency of EM waves.

We often refer to the speed of EM radiation as the "speed of light", although the visible light is only a small portion of EM radiation produced by the Sun. Therefore, we are unable to see all phenomena occurring around us because of our limited ability to detect all kinds of EM waves.

### Example 1

A yellow light ray has a wavelength of 600 nm. What is its frequency in Hz? (1 nm = 10-9 m).

### Solution 1

First, we must write the speed of EM waves (speed of light) in standard form. Thus, we have

c = 300 000 km/s
= 300 000 000 m/s
= 3 × 108 m/s

Also, we have for the wavelength of the yellow light ray:

λ = 600 nm
= 600 × 10-9 m
= 6 × 10-7 m

Applying the equation of waves for the EM radiation

c = λ × f

we obtain for the frequency of the given yellow light ray

f = c/λ
= (3 × 108 m/s)/(6 × 10-7 m)
= 0.5 × 108 - (-7) Hz
= 0.5 × 1015 Hz
= 5 × 1014 Hz

As you see, this is a very big value. This is the reason why we are not able to detect the oscillations of the light rays but we see them only as straight lines.

## Electromagnetic Spectrum

The range of EM waves from the shortest to the longest is known as "electromagnetic spectrum". We can classify EM waves from the least powerful to the most powerful (i.e. from the least energetic to the most energetic) based on two criteria:

a) According to the wavelength. In this classification, the first (the least powerful) waves are those with the longest wavelength because it is frequency the quantity which varies directly with energy. Based on the equation of waves where wavelength and frequency are in inverse variation, it is easy to deduce that energy and wavelength are inversely proportional to each other. Look at the figure: Based on wavelengths, EM waves are classified according to the following subcategories (all values are approximate because the limits in each category are intertwined.

These are the least powerful (energetic) waves although their amplitude is the largest. This is because energy varies directly with amplitude but also it varies directly with the square of frequency (i.e. inversely with the square of wavelength). This means frequency (and wavelength) affect the energy of EM waves more than amplitude.

The range of wavelengths for radio waves vary from 106 m to 10-1 m. Radio waves have the advantage of propagation in long distances due to their large amplitude. Therefore, they are mostly used for communication purposes.

### 2. Micro waves

The range of wavelengths for these waves vary from 10-1 m to 10-5 m. Wi-fi and microwave ovens are examples of microwaves use in technology.

These waves are perceived as heat. Thus, a hot object emits a lot of IR radiation while a cold object emits less IR radiation. Devices controlled remotely through sensors such as TV remote etc. are all examples of the IR radiation use in technology. Also, thermal cameras which enforce the weak IR radiation emitted by human body to make it visible, are another example of the IR radiation use in technology.

The range of IR radiation wavelength vary from 10-5 m to 7 × 10-7 m (700 nm).

### 4. Visible light

This is the only part of EM radiation we are able to see at naked eye. The range of wavelengths for visible light is very narrow. It varies from 7 × 10-7 m (700 nm) to 4 × 10-7 m (400 nm). We will discuss in particular about visible light in the our Physics tutorial on the "Features of Light".

They are EM waves that are more powerful than the visible light, and thus we are not able to see them. (Remember the ultrasounds which are powerful sounds we are not able to hear. This is a similar situation.) Therefore, we must avoid the exposure for long periods in direct sunlight because we cannot see UV radiation falling on our skin, so this may cause harm in our body as they have ability to penetrate the skin layer and burn it. Most UV radiation is filtered by atmosphere (by ozone layer in particular); however, not all UV radiation is filtered, especially in regions where the ozone layer is less dense.

The range of wavelengths for UV radiation varies from 4 × 10-7 m to 10-10 m.

### 6. X-rays

These are powerful EM waves which we cannot see. X-rays have the ability to penetrate the human tissue; therefore, they are used in imaging technology such as in radiography.

We must avoid the exposure to X-rays as they may cause long-term or permanent damage to our body. A large number of diseases are associated with the harm caused by exposure to radiation.

The range of wavelengths for X-rays varies from 10-10 m to 10-12 m.

### 7. Gamma (γ) rays

These are the most powerful EM waves. It is absolutely prohibited the exposure even for a short time to these waves as they have the ability to penetrate the entire human body including the bones. Some radioactive elements such as Uranium and Plutonium have the ability to emit gamma radiation by themselves. This is the reason why they are so dangerous.

Gamma rays carry a lot of energy. Therefore, they are used in nuclear reactors to produce energy or nuclear weapons in a controllable way.

The range of wavelengths for γ-rays varies from 10-12 m to 10-16 m.

b)According to the frequency. You can find the corresponding range of frequencies for each category of EM waves based on the equation of waves

c = λ × f

where c = constant = 3 × 108 m/s. In this way, you find the following values:

1. Radio waves. Since the range of wavelengths for these waves is 10-1 m ≤ λ ≤ 106 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 102 Hz ≤ f ≤ 109 Hz.
2. Microwaves. Since the range of wavelengths for these waves is 10-5 m ≤ λ ≤ 10-1 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 109 Hz ≤ f ≤ 1013 Hz.
3. Infrared Radiation. Since the range of wavelengths for these waves is 7 × 10-7 m ≤ λ ≤ 10-5 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 1013 Hz ≤ f ≤ 4.5 × 1014 Hz.
4. Visible Light. Since the range of wavelengths for these waves is 4 × 10-7 m ≤ λ ≤ 7 × 10-7 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 4.5 × 1014 Hz ≤ f ≤ 7.5 × 1014 Hz.
5. Ultraviolet radiation. Since the range of wavelengths for these waves is 4 × 10-7 m ≤ λ ≤ 10-10 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 7.5 × 1014 Hz ≤ f ≤ 1018 Hz.
6. X-rays. Since the range of wavelengths for these waves is 10-10 m ≤ λ ≤ 10-12 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 1018 Hz ≤ f ≤ 1020 Hz.
7. Gamma rays. Since the range of wavelengths for these waves is 10-12 m ≤ λ ≤ 10-16 m, we obtain for the range of corresponding frequencies (neglecting the constants before the powers of ten): 1020 Hz ≤ f ≤ 1024 Hz.

In the figure below, a double classification of EM waves based on the frequency and wavelength is shown. ### Example 2

How many times (at minimum) must a thermal camera enforce the body radiation to make humans visible during the night? Take the average frequency of images a thermal camera can record equal to 5 × 1013 Hz.

### Solution 2

A thermal camera must produce images at least at the minimum part of visible light, i.e. images of minimum frequency of 4.5 × 1014 Hz. These images are

4.5 × 1014/5 × 1013 = 9 times

more powerful that the real images recorded by the thermal camera. Therefore, such camera must enforce the images by 9 times to make them visible.

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