Struggling to understand the concept of this question (ice cube in water optics question)

[murshiddreamengineer]

TL;DR Summary: I came across this question from a Sri Lankan A-level textbook.

Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water.

I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an idea, or do we need more information to approach this question?

 

[.Scott]

I believe the author intends for the observer to be looking down into the water from above the water.

There is enough information provided in the problem statement.
You should have been given an equation for computing the actual depth given the apparent depth when viewing down through a transparent material.

Here is a link: Apparent Depth

 

[murshiddreamengineer]

I believe the author intends for the observer to be looking down into the water from above the water.

There is enough information provided in the problem statement.
You should have been given an equation for computing the actual depth given the apparent depth when viewing down through a transparent material.

Here is a link: Apparent Depth

I'm sorry, the question says that the ice cube is partially immersed (floating). I mistakenly say immersed

 

[.Scott]

Are you quoting the problem statement precisely?

If so, we are supposed to presume that this ice cube is a real cube - and therefore, 10 cm high.
Once again, the phrase "from the water" is very ambiguous - it could mean from the surface of the water or from beneath the water surface or from over the water.

I take it to mean from "over the water", because anything else would require more explanation.

You will still need that apparent depth formula.
You might want to start by calculating what that 10 cm height would look like if the entire cube was submerged.

Then, it will just be a matter of determining what portion is actually submerged.

 

[kuruman]

I believe the author intends for the observer to be looking down into the water from above the water.

In that case how does one interpret "from the water" as in "An observer observes the ice cube from the water"? Is the observer immersed in the water or is something lost in translation?

To @murshiddreamengineer: Is there a drawing or diagram that accompanies this problem?

On edit: I see that @.Scott has the same question.

 

[haruspex]

Is the observer immersed in the water

Wouldn’t that make the height seem greater?

 

[murshiddreamengineer]

In that case how does one interpret "from the water" as in "An observer observes the ice cube from the water"? Is the observer immersed in the water or is something lost in translation?

To @murshiddreamengineer: Is there a drawing or diagram that accompanies this problem?

On edit: I see that @.Scott has the same question.

yes, he is in the water and look the ice cube

 

[kuruman]

Wouldn’t that make the height seem greater?

Yes it would make the height seem greater. I assume that "height" means the dimension perpendicular to the surface of the water. Here, we are told that the "length" of 10 cm appears to the observer as 7.75 cm. Presumably "length" is perpendicular to "height" hence parallel to the surface. I am trying to visualize the line of sight of the observer.

I cannot resist adding a thought I just had. This could be trick question the answer to which is, "An ice cube with a length of 10 cm has a height also of 10 cm because it's a cube, no?"

On Edit: OK the observer is in the water.

 

[murshiddreamengineer]

yes, he is in the water, and look at the ice cube

Actually, it is a cuboid.

 

[kuruman]

View attachment 366074Actually, it is a cuboid.

This clears it up. Thank you. Look up "Apparent depth at near normal incidence" and use the same reasoning but from below the surface.

 

[haruspex]

This clears it up. Thank you. Look up "Apparent depth at near normal incidence" and use the same reasoning but from below the surface.

I still fail to see how it could appear to be less than the true height when viewed from the denser medium.

 

[.Scott]

View attachment 366074Actually, it is a cuboid.

The reason I didn't think the problem would be set up this way is that now you are using a lens system intended for air and putting it in direct contact with the water.

This drawing also clears up another issue - "long" means "high".

Do we get to assert that any reasonable human observer would be wearing swimming goggles?
If so, you can use the same equations that would be used for the view from above.

If not, then I believe the problem is understated. I think that you would need to consider the curvature of the lens surface in contact with the water - which may vary based on how the viewer is attempting to focus,

 

[jbriggs444]

yes, he is in the water and look the ice cube

Anyone with eyes that function underwater and using stereoscopic binocular vision for distance detection will correctly determine underwater distances. It is simple triangulation irrespective of how one brings the two images into focus.

I agree with @.Scott about the manner in which being underwater could affect range detection by focal distance.

 

[kuruman]

I still fail to see how it could appear to be less than the true height when viewed from the denser medium.

So do I. That is why I asked for clarification about the point of view and suggested that OP considers the "apparent depth" from the other side.

 

[murshiddreamengineer]

The reason I didn't think the problem would be set up this way is that now you are using a lens system intended for air and putting it in direct contact with the water.

This drawing also clears up another issue - "long" means "high".

Do we get to assert that any reasonable human observer would be wearing swimming goggles?
If so, you can use the same equations that would be used for the view from above.

If not, then I believe the problem is understated. I think that you would need to consider the curvature of the lens surface in contact with the water - which may vary based on how the viewer is attempting to focus,

Even if we assume he is wearing goggles. How does the apparent height depend on the height of ice cuboid immersed in the water

 

[kuruman]

Even if we assume he is wearing goggles. How does the apparent height depend on the height of ice cuboid immersed in the water

Look up the derivation for apparent depth. Adapt it for the case where the “depth” is viewed from the other side.

 

[murshiddreamengineer]

Look up the derivation for apparent depth. Adapt it for the case where the “depth” is viewed from the other side.

I do not understand what you mean by "viewed from the other side"

 

[.Scott]

I do not understand what you mean by "viewed from the other side"

What is significant about looking down from above is that you are looking at the water through a horizontal surface between the air and the water. Looking up through such a horizontal surface will produce the same effects.

 

[haruspex]

Even if we assume he is wearing goggles. How does the apparent height depend on the height of ice cuboid immersed in the water

The apparent height of the whole block is the sum of the apparent height of the submerged portion and the apparent height of the exposed portion. Ignoring issues to do with the eye/water interface, the apparent height of the submerged portion would be the true height while that of the exposed portion would be altered by refraction at the air/water interface.
Thus, the change in apparent height of the whole block depends on what fraction is submerged.