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Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

 

$$n=n_0-\alpha h$$

 

with condition $\frac{\alpha h}{n_0}\ll1$

 

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

 

$$n=n_0-\alpha h$$

 

with condition $\frac{\alpha h}{n_0}\ll1$

 

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

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BMS
BMS
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Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)

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Martin Gales
Martin Gales
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A beam of light, traveling around a planet

Some time ago, I happened to have found one problem:

The refractive index of the planet's atmosphere decreases with height above the surface under the following law:

$$n=n_0-\alpha h$$

with condition $\frac{\alpha h}{n_0}\ll1$

Find the altitude $H$ above the surface of the planet, where a ray, emitted horizontally, will bypass the planet, remaining at this elevation. Radius of the planet is $R$.

Since optics is not my field I decided to ask here. What would be the height $H$ for the Earth? (approximately)