EasyPhysicsHigh School (9–10)Optics › Light in the AtmosphereConceptual

Light from a star that is truly 70° from overhead comes down through the air.

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Light from a star that is truly $70^\circ$ from overhead comes down through the air. Treat the air as flat layers, with $n = 1.0003$ at the ground, so that $\sin(70^\circ) = 1.0003 \times \sin(\text{angle seen})$ . How much higher does the star look, in minutes of arc ( $60$ minutes $= 1^\circ$ )?

Need a reminder? The key ideaShow

The air is denser near the ground, so starlight bends as it comes down. Stars look higher, and they twinkle as the air moves. The Sun is seen about $2\ \text{min}$ before true sunrise and $2\ \text{min}$ after true sunset.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

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