What is the distance between the ship and the submarine using a laser?

[johnsy123]

In the figure, a laser positioned on a ship is used to communicate with a small two-man research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 76 m deep and has an index of refraction of 1.33. How far horizontally is the submarine from the side of the ship?

-I am not sure weather to use the mirror equation or not. I have tired to figure out the angle the laser makes with the vertical and then combined that into a big triangle with height of 88 to find the horizontal distance but that didn't seem to get the right answer.

 

[Ibix]

What happens to a light ray entering water (or almost any transparent medium, for that matter)?

 

[johnsy123]

It bends.

 

[johnsy123]

i also attempted using snells law to find the refracted angle...

 

[Ibix]

Right. You should be able to work out the angle of incidence, and Snell's Law gives you the angle of the ray in the water. Add the refracted ray to the diagram, and you should be able to see how to calculate the distance.

Remember to be careful about which angle Snell's Law needs.

 

[johnsy123]

Yes i did that and i still didn't get the correct answer.

 

[Doc Al]

Show exactly what you did.

 

[Ibix]

As Doc Al says, show your working. We're guessing what you did, and we could be here all day.

I will make one more guess, though. You said you made one big triangle, but there are two non-congruent triangles - ship-to-surface and surface-to-sub. Are you treating them separately?