Neglecting the curvature of the earth, compute the deviation...

Neglecting the curvature of the earth, compute the deviation of starlight incident at an angle of $80^{\circ}$ (the star is $10^{\circ}$ above the horizon) on the top of the earth's atmosphere if the index of refraction of the air at the earth's surface is 1.00030 .

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Key Concepts

Snell's Law

Snell’s Law relates the angle of incidence and the angle of refraction when light passes between two media with different refractive indices. It is expressed as n? sin?? = n? sin?? and is fundamental in calculating how light bends at the interface between, in this context, the vacuum of space and the Earth’s atmosphere.

Index of Refraction

The index of refraction is a measure of how much the speed of light is reduced inside a medium compared to the speed of light in a vacuum. In the context of atmospheric refraction, even a small deviation from unity, as in the given index of 1.00030 for air, can lead to measurable bending of starlight.

Atmospheric Refraction

Atmospheric refraction refers to the bending of light as it travels through the Earth’s atmosphere due to the gradient in the air’s refractive index. This phenomenon causes the apparent position of stars and other celestial bodies to deviate slightly from their true positions.

Planar Approximation (Neglecting Curvature)

In many optical problems, including this one, the Earth’s curvature is neglected to simplify the analysis. This planar approximation allows us to treat the atmosphere as a flat layer, making it easier to apply Snell’s Law to compute the deviation of light as it enters the atmosphere.

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