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# Speed of Light

## Light is the fastest thing in the universe and always has the same speed in a vacuum.

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Speed of Light

Light travels at 3×108m/s\begin{align*} 3 \times 10^8 \text{m/s}\end{align*}. We call this value c. Light can never travel at any other speed. Although when light travels through materials, due to scattering and absorption it appears that light is going slightly slower (see refraction lesson for more detail). A light year is the amount of distance light covers in a time of one year. The value of one light year is simply the speed of light multiplied by the number of seconds in a year and is roughly equal to 9.4×1015m\begin{align*} 9.4 \times 10^{15} \text{m} \end{align*} . Viewing distant stars is looking back in time. The stars we see are many thousands of light years away, which means the light takes many thousands of years to reach us. Thus the stars we see in the sky are how they looked thousands of years ago.

Key Equations

D=ct\begin{align*} D = ct \end{align*}; distance is equal to the speed of light multiplied by the time it has traveled

#### Example

How long after texting your friend on Mars will he receive it?

Mars is a distance of 3.1×1011m\begin{align*} 3.1 \times 10^{11} \text{m}\end{align*}. Thus, using the equation t=Dc=3.1×1011m3×108m/s\begin{align*} t = \frac{D}{c} = \frac{3.1 \times 10^{11} \text{m}}{3 \times 10^8 \text{m/s}}\end{align*} = 1033 seconds or about 17 minutes.

### Review

1. Our sun is 8 “light minutes” from earth.
1. Using the speed of light as c\begin{align*}c\end{align*} calculate the earth-sun distance in m\begin{align*}m\end{align*}, then convert it to miles (one mile = 1609 m)
2. The nearest galaxy to our Milky Way is the Andromeda Galaxy, 2 million light years away. How far away is the Andromeda Galaxy in miles?
2. The Canis Major Dwarf galaxy is 2.364×1020m\begin{align*} 2.364 \times 10^{20} \text{m} \end{align*} .
1. How far is it in light years?
2. If the galaxy were to disappear, how long until we notice it vanish on Earth?
3. Light does not travel infinitely fast – its speed in a vacuum is 3×108m/s\begin{align*}3 \times 10^8 \text{m/s} \end{align*}. We measure very large astronomical distances in “light years” (LY) – the distance light travels in one year. The closest star beyond our sun is Alpha Centauri, 4 LY away. Some distant quasars are 2 billion LY away. Why do astronomers say that to look at these distant objects is to look back in time? Explain briefly.

1. a. 1.44×1011m\begin{align*} 1.44 \times 10^{11} \text{m} \end{align*} b. 8.95×107miles\begin{align*} 8.95 \times 10^{7} \text{miles} \end{align*}

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