Converging lens becomes Diverging lens

[A_lilah]

Homework Statement

Can a converging lens in air become a diverging lens in a different refractive medium?

Homework Equations

n1sin(θ1)=n2sin(θ2)

The Attempt at a Solution

I was thinking that it would not matter what medium the lens was in, as light would still hit the lens the same way and converge (I was trying to picture using a magnifying glass underwater- it would still magnify, just a bit less because the light would bend less). My question comes when trying to figure out the angles of refraction when the lens is in a medium whose index of refraction is greater than glass (for example, what would happen if there was a magnifying glass inside a diamond, which has an n= 2.419 according to wikipedia):

2.419sin(45) = 1.5sin(θ)
solving for θ:
θ = sin-1(2.419sin(45)/1.5) = sin-1(1.710/1.5)
1.710/1.5 is obviously greater than 1, which is not in sine's domain... I just don't understand what that means.
Thanks for the help :)

 

[Gear.0]

Why is your incident angle 90 degrees?
That would mean that the incident ray is traveling ON the interface.
zero degrees would be straight down, which wouldn't give any refraction.
At least I am assuming that you have the ray going from the media n=2.419 --> n=1.5 Because, you said you wanted to see if a thicker media would result in divergence.

Perhaps what you were trying to do is find the maximum angle (or whatever it is called) that would be done by setting the other angle to 90. If this is what you were trying to do you had it backwards.
2.419sin(θ)=1.5sin(90)
θ = about 38.3 degrees.

Anything larger than that and the light ray will actually reflect, so you have to use an angle between 0 and 38.3 degrees. You were using 90 so that is the problem.
But, just thinking about it, I believe it is possible to have a converging lens become a diverging lens in the proper material. It might have to be made thicker then normal though, not sure.

 

[A_lilah]

Oh! So the angle doesn't work because the light is not all refracting to the other side at that angle~ some is reflecting. :) Thanks!
I still am not exactly sure how to tell if a converging lens will become a diverging one in a different medium...

 

[Gear.0]

Draw a diagram. A converging lens bulges out from the middle.
Just draw a single ray near either the top or the bottom of the lens. First draw it for air, just to see how the process works and you should see that it converges. Then once you have it down, draw it for a thicker medium and you should see the resultant ray bend outward, diverging.

Remember to draw a new normal to for each surface where the light ray hits the interface between media, and that when the ray is entering a medium denser than the one it is in, it bends toward the normal, when it is leaving a dense medium into a less dense medium it bends away from the normal.

 

[A_lilah]

Thanks for your help :)