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## Magnifying Sunlight

If you've ever experimented with a magnifying glass in sunlight, you may know that sunlight is capable of lighting twigs or hay on fire with the right tools. A magnifying glass can focus sunlight so that the energy which would be spread out over a wide area is delivered to a much smaller point.

This raises a natural question: if we can build an arbitrarily large magnifying glass, is there a limit to the temperature that could be reached?

As it turns out, there are limits to how much sunlight can be concentrated — focused sunlight can't heat something up to an infinitely high temperature. A lens can focus light from a single direction to a point.

You might be tempted to design giant magnifying glass to focus as much of the Sun's energy as possible. But if two sources of light are coming from different directions, then the lens will focus them onto two different points.

The Sun is not a perfect point in the sky — its cross-section is a disc. Light from different parts of the solar disc come from slightly different directions, which means that it can't all be focused down to a single point. Making the magnifying glass bigger spreads out the area of focus. This means the energy is more widely distributed, and the temperature at the ground may not be getting higher.

While this is useful for understanding why sunlight can't be focused to an arbitrarily small point, a simpler approach for answering the question of "what is the hottest temperature we could reach?" is to consider that (in the absence of external energy input) heat flows from higher temperature to lower temperature.

If heat could flow from lower temperatures to higher temperatures without external energy input, you could build a perpetual motion machine.

The sunlight that shines out from the surface of the Sun is heat in the form of radiation, so there are physical limits to how much that sunlight can heat something up.

# Today's Challenge

A magnifying glass can be a helpful survival tool, since magnified sunlight can start a campfire. With the right magnifying glass, you could reach even higher temperatures.

What is the highest temperature you could reach using sunlight and an optically perfect magnifying glass?

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