Light and Electromagnetic Waves

Light from the Sun crosses roughly $150$ million kilometers of virtually empty space to reach Earth.

1. a) Does light need a material medium to travel through?
2. b) What are waves called that, like light, can travel through a vacuum?
3. c) If a distant star were to explode, what would we perceive from Earth: its light, its bang, or both? Justify your answer.

The speed of light in a vacuum is $c = 3\times10^{8}\ \text{m/s}$.

1. a) What distance does light travel in one second? Express it in meters and in kilometers.
2. b) The Earth's circumference is about $40\,000\ \text{km}$: how many times could light travel around the planet in one second?

The Moon is about $384\,000\ \text{km}$ from Earth. How long does it take for its light to reach us? Give your answer to one decimal place. ($c = 3\times10^{5}\ \text{km/s}$.)

We cannot see what is around a corner, although we can hear noises coming from there.

1. a) What does this tell us about the way light travels?
2. b) Explain how the shadow of your hand is formed on the wall.
3. c) Name an astronomical phenomenon that is explained in the same way.

On passing through a prism, white sunlight splits into a band of colors like a rainbow.

1. a) Name the colors of this band in order.
2. b) What invisible radiation exists beyond red and beyond violet? Give an example of an application for each.
3. c) Do red light and violet light travel at different speeds in a vacuum?

A T-shirt looks red under white sunlight.

1. a) Explain what the fabric does with the different components of white light so that we see it as red.
2. b) Predict what color that T-shirt will appear in a room illuminated only with green light and justify your answer.
3. c) What color will a white T-shirt appear in that same room? Give reasons for your answer.

Red light has a wavelength of around $6\times10^{-7}\ \text{m}$ and microwave oven waves, $0.12\ \text{m}$. All electromagnetic waves travel in a vacuum at $c = 3\times10^{8}\ \text{m/s}$.

1. a) Calculate the frequency of red light and that of microwaves using $c = \lambda \times f$.
2. b) Which of the two has a higher frequency?
3. c) Complete the rule and justify it using the formula: "the longer the wavelength, the $\dots$ the frequency".
4. d) Order these types of radiation from lowest to highest frequency: X-rays, infrared, visible light and radio waves.

Match each electromagnetic radiation with its application and write down the five complete pairs:

1. a) X-rays.
2. b) Infrared.
3. c) Microwaves.
4. d) Ultraviolet.
5. e) Radio waves.

Applications: an X-ray at the hospital, the TV remote control, heating food in an oven, detecting counterfeit banknotes, and listening to the car radio station.

What do all these types of radiation have in common?

Light travels through an optical fiber at $2\times10^{8}\ \text{m/s}$.

1. a) How long does it take for a pulse of light to travel $100\ \text{km}$ of fiber? Express your answer in standard form.
2. b) Convert the result to milliseconds.
3. c) Explain why optical fiber transmits internet connections with so little lag.

All electromagnetic radiation travels at the same speed in a vacuum, but the energy of each photon increases with frequency, and very high-frequency radiation, such as X-rays, is highly penetrating.

1. a) Order from lowest to highest frequency: infrared, ultraviolet, visible light and X-rays.
2. b) Explain why sunglasses and sunscreens mainly filter ultraviolet radiation and not infrared.
3. c) Why do healthcare staff shield themselves behind a lead barrier when taking X-rays, and why is the number of X-rays given to a patient limited?
4. d) Thermal imaging cameras detect the infrared emitted by hot bodies: explain why they are useful for locating people in the dark.

Sunlight takes about $8\ \text{min}$ and $20\ \text{s}$ to reach Earth.

1. a) Express this time in seconds.
2. b) Calculate the distance between the Sun and Earth in kilometers, using $c = 3\times10^{5}\ \text{km/s}$, and express it in scientific notation.

A light year is the distance light travels in one year: about $9.5\times10^{12}\ \text{km}$. Proxima Centauri, the closest star to the Sun, is $4.2$ light years away.

1. a) Calculate this distance in kilometers, in scientific notation.
2. b) How long does it take for light from Proxima Centauri to reach us?

The Apollo mission astronauts spoke with mission control in Houston by radio, and radio waves travel at the speed of light. The Moon is $384\,000\ \text{km}$ away.

1. a) How long does a question from Houston take to reach the Moon?
2. b) What is the minimum time between Houston asking the question and hearing the astronaut's answer?
3. c) Why do we say "at least"?

Light from Sirius, the brightest star in the night sky, takes $8.6$ years to reach Earth.

1. a) How far away is Sirius, expressed in light years?
2. b) When you observe it tonight, do you see Sirius as it is now or as it was some time ago? Explain your answer.
3. c) What do astronomers mean when they say that looking far away with a telescope is looking into the past?

Let us calculate how many kilometers a light year is.

1. a) How many seconds are in a year of $365$ days? Express your answer in scientific notation.
2. b) Multiply this time by the speed of light ($c = 3\times10^{8}\ \text{m/s}$) and give the distance in meters and in kilometers.
3. c) The star Vega is about $25$ light years away: calculate this distance in kilometers.

Betelgeuse, a star in the constellation of Orion, is about $640$ light years away and astronomers expect it to explode as a supernova one day.

1. a) If telescopes were to observe the explosion tomorrow, when did it actually occur? What was happening, approximately, in Earth's history at that time?
2. b) If the explosion actually occurred today, when would the news reach Earth?
3. c) Explain why astronomers compare observing very distant objects to receiving a letter written a long time ago.

The Apollo mission astronauts left mirror panels on the Moon. A laser pulse sent from an observatory reflects off them and returns $2.56\ \text{s}$ later. The Moon is $384\,000\ \text{km}$ away. The diagram shows the path of the light pulse.

1. a) What total distance does the light pulse travel?
2. b) Calculate the speed of light obtained from this experiment and express it in $\text{km/s}$ and in $\text{m/s}$.
3. c) Explain why the speed of light cannot be measured using a torch and a stopwatch between the two ends of the school playground.

A torch beam strikes a bathroom mirror making an angle of $30^\circ$ with the normal, the line perpendicular to the mirror. The figure shows the incident ray on the mirror.

1. a) At what angle is the ray reflected, measured from the normal?
2. b) State the law of reflection in your own words.
3. c) Draw the mirror, normal, incident ray and reflected ray in your notebook, and mark the angles.

You can do it on paper and send a photo with your answer.

A light ray strikes a plane mirror making an angle of $40^\circ$ with the mirror surface. The figure shows the incident ray on the mirror.

1. a) What angle does the incident ray make with the normal?
2. b) What is the angle of reflection, measured from the normal?
3. c) Draw the situation in your notebook and label all the angles.

You can do it on paper and send a photo with your answer.

A simple periscope has two parallel plane mirrors, each inclined at $45^\circ$ to the horizontal, one at the top and one at the bottom of the tube. The figure shows the periscope with its two mirrors.

1. a) Draw in your notebook the path of a light ray entering horizontally at the top mirror until it reaches the eye, applying the law of reflection at each mirror.
2. b) What angle does the ray make with the normal at each mirror? By how much does the ray turn at each reflection?
3. c) Explain why the ray reaching the eye is horizontal and parallel to the ray that entered.
4. d) State a practical application of a periscope.

You can do it on paper and send a photo with your answer.

A straw inside a glass of water appears bent right at the water surface. The figure shows what is observed.

1. a) Is the straw actually bent? Explain what happens.
2. b) What happens to the light coming from the submerged part of the straw as it passes from water to air?
3. c) What is this phenomenon called?

Light travels through water at about $225\,000\ \text{km/s}$, slower than in air, where it travels at about $300\,000\ \text{km/s}$. The figure shows the change in direction of the ray as it passes from air to water.

1. a) Calculate how many times faster light is in air than in water, to one decimal place.
2. b) On passing from air to water, the light ray bends towards the normal: relate this change of direction to the change in speed and name the phenomenon.
3. c) Using this, explain why a straw in a glass of water appears bent.

A fisherman standing on the bank sees a fish underwater.

1. a) Light rays leaving the fish pass from water into air, where they travel faster: do they bend towards or away from the normal upon reaching the surface?
2. b) Our brain interprets light as having travelled in a straight line: explain why the fish appears closer to the surface than it actually is.
3. c) Draw the rays and the apparent position of the fish in your notebook.
4. d) Why, when spearfishing, must you aim below where the fish appears to be?

You can do it on paper and send a photo with your answer.

After a summer storm, with the Sun low behind you and the rain in front, a rainbow appears.

1. a) Explain what happens to sunlight as it enters each raindrop, reaches the back of the drop and exits it, naming the phenomena involved.
2. b) Each color refracts at a slightly different angle: what is the separation of white light into colors called?
3. c) Explain why, to see a rainbow, the Sun must be behind you and the rain in front.
4. d) The arc is visible because only the raindrops positioned at a certain angle relative to the direction of the Sun reflect light back to you: explain why this forms a curve.