Light and depth

[chiddler]

If the index of refraction doubles for a liquid in which a coin is submerged, the apparent depth of the coin will increase or decrease?

A larger n value means it will refract more towards the normal and therefore will appear deeper than it really is. So apparent depth increases.

But this is wrong because it will decrease according to TBR answer.

Halp, please.

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[MedPR]

If the index of refraction doubles for a liquid in which a coin is submerged, the apparent depth of the coin will increase or decrease?

A larger n value means it will refract more towards the normal and therefore will appear deeper than it really is. So apparent depth increases.

But this is wrong because it will decrease according to TBR answer.

Halp, please.

The apparent depth corresponds to the actual depth by:

apparent = actual * nair/nwater.

So when the nwater doubles, the apparent depth decreases. I think you're getting confused by which light ray corresponds to the apparent object and which corresponds to the actual object.

Sorry, I should show how you get to that equation I mentioned above. Start with snell's law.

n1sinθ1=n2sinθ2

sinθ=o/h

n1(o1/h1)=n2(o2/h2) where o1=o2. Why? When you look at an object that is submerged in water, you see it as if the light didn't refract at all. The depth is different, but the x-distance is exactly the same as the actual object. In other words, the apparent object is directly above the actual object. Remember that sinθ is opposite/hypotenuse, and in this case it is x/hypotenuse because the opposite side is the x (not the y as it almost always is in other situations). Now you can cancel out your o1 and o2 and be left with n1/h1=n2/h2 where h1 = apparent depth and h2 = actual depth. Rearrange the equation to n1=h1n2/h2, and then to h1=n1h2/n2. So as you increase n2 (water, in this case) without moving the object, you decrease h1 (apparent).

 

[chiddler]

Isn't that illustrating that depth increases? Where the two dotted lines converge is the actual depth, right? This is where the fish really is.

So increasing n will cause the solid lines to diverge more before they meet the eye. To me this appears that this causes the apparent depth to increase. The fish appears to be deeper.

 

[chiddler]

reading edit. moment.

 

[MedPR]

Isn't that illustrating that depth increases? Where the two dotted lines converge is the actual depth, right? This is where the fish really is.

So increasing n will cause the solid lines to diverge more before they meet the eye. To me this appears that this causes the apparent depth to increase. The fish appears to be deeper.

No the dotted lines (in both pictures) correspond to the apparent depth. Whenever n2 > n1, the object is deeper than it appears to be. Go fill your kitchen sink with water and drop a coin in it. Then, ignore your intuition and just reach in and grab the coin where it appears to be. You won't grab it, because you won't have reached deep enough. I'm not trying to be a dick, I've actually done some simple home experiments to prove mcat physics to myself (like how looking at an image 10m away from a plane mirror is equivalent to looking at the same image from 20m away) and it has helped.

I think the second part of the first post is easier to understand so just ignore part 1, it's the same thing just in a different form.

 

[chiddler]

No the dotted lines (in both pictures) correspond to the apparent depth. Whenever n2 > n1, the object is deeper than it appears to be. Go fill your kitchen sink with water and drop a coin in it. Then, ignore your intuition and just reach in and grab the coin where it appears to be. You won't grab it, because you won't have reached deep enough. I'm not trying to be a dick, I've actually done some simple home experiments to prove mcat physics to myself (like how looking at an image 10m away from a plane mirror is equivalent to looking at the same image from 20m away) and it has helped.

I think the second part of the first post is easier to understand so just ignore part 1, it's the same thing just in a different form.

yes i like the second image a lot more. I think I understand this.

no offense taken. thanks.

 

[MedPR]

yes i like the second image a lot more. I think I understand this.

no offense taken. thanks.

Happy to help. It might help to remember that no matter what the index of refraction changes to, the object is always at the same depth.

 

[chiddler]

yup yup. did test numbers and well understood. thanks again.

 

[milski]

My non-scientific way for this:

We start with air-air. Apparent depth is correct. Now we replace the second media with water, which has higher refracting index. If you ever have been in a shallow pool, you'd know that the apparent depth decreases. Thus increasing the refracting index decreases the apparent depth.

 

[pfaction]

People, this is why you should always draw pictures even on the exam. Reading comprehension f'ed me over, and this did too--by drawing out the picture I realized it appeared shallower!