[DoctorBeaver (OP)]

Seany's post about a laser his friend bought prompted this question.

http://www.thenakedscientists.com/forum/index.php?topic=13568.0

Assuming this device really does have a range of 50 miles and was shone horizontally from the waist (say 3ft above the ground), at what altitude would the beam be 50 miles away?

[Seany]

Nice question Doc! [] LOL

[Karen W.]

Yes indeed!

[DoctorBeaver (OP)]

The relevance of diegoqing's reply is...?  []

[Seany]

Ermm.. Like.. Because

If you buy some Nike trainers, you feel more lively and jolly and moveable.. So you jump up and down with Michael Jordan's nike shoes and you see how high the laser is..

I donno!! []

[Karen W.]

Well I think his shoes allowed me to give a good kick!! LOL!

[DoctorBeaver (OP)]

Anyone reading this will wonder what the hell we're talking about. They won't realise a post has been deleted. Well, they will now because I've mentioned it. But they won't know what it said.

[Seany]

LOL, something about nike trainers []

[turnipsock]

It will be 0.35 of a mile, plus 3 ft.

[Seany]

It will be 0.35 of a mile, plus 3 ft.

How did you work this out? []

[Seany]

Seany's post about a laser his friend bought prompted this question.

http://www.thenakedscientists.com/forum/index.php?topic=13568.0

Assuming this device really does have a range of 50 miles and was shone horizontally from the waist (say 3ft above the ground), at what altitude would the beam be 50 miles away?

Doesn't it also differ with the quality of the laser? Better lasers spread less than others//

[turnipsock]

It will be 0.35 of a mile, plus 3 ft.

How did you work this out? []

The circumference of the earth is 360x60=21,600 miles. That is because one mile equals 1 minute of a degree.

From that you can calculate the radius of the earth.

Then it is just a right angled triangle after that where one side is the radius of the earth, another side is 50 miles and you can calculate the length of the hypotenuse. The altitude is the difference between the hypotenuse and the radius of the earth.

A similar thing occurs when ships have to calculate at what distance they should be able to see a lighthouse.

[ukmicky]

http://newton.ex.ac.uk/research/qsystems/people/sque/physics/horizon/

[DoctorBeaver (OP)]

The circumference of the earth is 360x60=21,600 miles.

No it isn't. The equatorial circumference is 24,901 miles, and the polar circumference is 24,859 miles.

Your error doesn't inspire me with confidence in your answer  []

[Seany]

[]

[Bored chemist]

There's another complication. The air is denser at lower altitudes and so it has a higher refractive index. This means that the light bends downwards slightly.

[Pumblechook]

If h is in meters, that makes the distance to the geometric horizon 3.57 km times the square root of the height of the eye in meters (or about 1.23 miles times the square root of the eye height in feet).   

= about 500 metres.  This is ignoring any bending and the fact that it is rarely clear enough.  A power light ot laser will help.  I saw the hills of North Wales (incl Great Orme) from near sea level at Blackpool last year at the distance is pretty well 50 miles.   

[DoctorBeaver (OP)]

Wouldn't the Earth's gravitational field pull the beam down too?

[Bored chemist]

The direct effect of gravity is pretty small but the effect of the refraction is significant. If the earth's atmosphere weree replaced by SO2 which has a slightly greater refractive index, the curvature due to refraction would be roughly the same as the curvature of the earth and light would go right round (ignoring any mountains).

[DoctorBeaver (OP)]

The direct effect of gravity is pretty small but the effect of the refraction is significant. If the earth's atmosphere weree replaced by SO2 which has a slightly greater refractive index, the curvature due to refraction would be roughly the same as the curvature of the earth and light would go right round (ignoring any mountains).

Oooh... that could be fun. I could shine a torch on my own ars back!