Calculating the Speed of Dolphins Seen Through a Glass Window

[sona1177]

Homework Statement

At a marine animal park, Alison is looking through a glass window and watching dolphins swim underwater. If the dolphin is swimming directly toward her at 15 m/s, how fast does the dolphin appear to be moving?

Homework Equations

v=15 m/s
I realize that due to the refraction of light coming off of the dolphin, the dolphin appears to be swimming slower than it actually is.

I am supposed to use the concept of the the refraction of light: Snell's Law, but I'm not really seeing how to approach the problem here.

The Attempt at a Solution

 

[Doc Al]

Hint: If the dolphin is a distance X behind the glass, what is the apparent distance behind the glass according to Alison?

 

[sona1177]

It's the same? X?

 

[Doc Al]

It's the same? X?

No. If it were the same, then the apparent speed would be the same as the actual speed.

Look up apparent depth.

 

[sona1177]

No. If it were the same, then the apparent speed would be the same as the actual speed.

Look up apparent depth.

I know that n=1.33 but what does that have to do with apparent depth?

 

[Doc Al]

I know that n=1.33 but what does that have to do with apparent depth?

Did you look it up?

 

[sona1177]

Yes. But the girl is not looking at the dolphin from an elevated position. The dolphin is swimming directly at her. I don't see how the depth is changing. I see how depth would be relevant if the girl were on top of a chair looking down, but she is at level with the dolphin.

 

[Doc Al]

Yes. But the girl is not looking at the dolphin from an elevated position. The dolphin is swimming directly at her. I don't see how the depth is changing. I see how depth would be relevant if the girl were on top of a chair looking down, but she is at level with the dolphin.

True, she's at the same horizontal level as the dolphin, but what matters is that the dolphin is behind a depth of water. Whether dolphin-water-girl form a vertical line (if she were looking down from above) or a horizontal line (like described here) doesn't matter. By 'depth' we mean the distance beyond the water surface--that surface could be horizontal or vertical--the light travels the same either way.

 

[sona1177]

Doc Al, could you give me a little more to go with here? I need at least a start.

 

[sona1177]

OK, say she is a distance X behind the glass. If I had the time, I could divide change in X over t, and get velocity. but I know nothing about time, all I know is the speed--15 m/s.

 

[sona1177]

There is also nothing about apparent depth in my text but doing just from looking at the web, I am getting the formula

Apparent depth= Actual depth(ref index of air/ref index of water)

But we don't know the actual depth here! :(

 

[Doc Al]

OK, say she is a distance X behind the glass. If I had the time, I could divide change in X over t, and get velocity. but I know nothing about time, all I know is the speed--15 m/s.

But you know that ΔX/Δt is the actual speed.

There is also nothing about apparent depth in my text but doing just from looking at the web, I am getting the formula

Apparent depth= Actual depth(ref index of air/ref index of water)

But we don't know the actual depth here! :(

Good! That formula is all you need.

If the dolphin is a distance X behind the glass, then the actual 'depth' is X. So what's the apparent depth (distance) in terms of X? Then you can compare the actual speed (ΔX/Δt) with the apparent speed.