Light

Light from the Sun crosses roughly $150$ million kilometres 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 $c = 3\cdot10^{8}\ \text{m/s}$.

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

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

1. a) Name the colours 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 colour that T-shirt will appear in a room illuminated only with green light and justify your answer.
3. c) What colour will a white T-shirt appear in that same room? Give reasons for your answer.

Red light has a wavelength of around $6\cdot10^{-7}\ \text{m}$ and microwave oven waves, $0,12\ \text{m}$. All electromagnetic waves travel in a vacuum at $c = 3\cdot10^{8}\ \text{m/s}$.

1. a) Calculate the frequency of red light and that of microwaves using $c = \lambda \cdot f$.
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.

A light year is the distance light travels in one year: about $9,5\cdot10^{12}\ \text{km}$. Proxima Centauri, the closest star to the Sun, is $4,2$ light years away.

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

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 kilometres a light year is.

1. a) How many seconds are in a year of $365$ days? Express your answer in standard form.
2. b) Multiply this time by the speed of light ($c = 3\cdot10^{8}\ \text{m/s}$) and give the distance in metres and in kilometres.
3. c) The star Vega is about $25$ light years away: calculate this distance in kilometres.

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.

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 colour refracts at a slightly different angle: what is the separation of white light into colours 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.

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