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Past exam problem. Was it wrong?

- Wed, 22 Sep 2021 01:11:00 EST hy/3H0ZK No.80065
File: 1632287460823.png -(7225B / 7.06KB, 352x277) Thumbnail displayed, click image for full size. Past exam problem. Was it wrong?
This is a question on a past exam at university. I never understood it and it continues to frustrate me because even if I can't come up with the right answer to a problem, I'll at least 'get' (understand) the proper answer when it is given. But not this one. Here it is:

You are spearfishing in waist-deep water when you spot a fish that appears to be 45° below the water and about 50cm underneath the surface. You recognize that the light coming from the fish to your eye has been refracted and you must therefore aim at some depth below where the fish appears to be. How far below where the fish appears to be should you aim?

n air = 1
n water = 1.35
angle 1 = 45 degrees
assume a flat interface

The first part of the answer given was about first finding the angle of refraction and then the remaining angle (90 degrees minus the angle of refraction).

The second part of the answer given was about finding the value for y.

The last part of the answer given was about using this y value and the remaining angle to find the value of x. So

tan a = x/50cm
x = 50tan(a)
x = 81.3cm

Now I get each part of this answer, I just don't see how it is correct.

This is because the y value here doesn't have to do with the actual fish's position, only its apparent position.

If we knew either how far down or away the fish actually was, then it would be easy to find the missing value because we also know the angle of refraction. But we know neither.

So even though its true that at 50cm away and at an angle of 58.42 degrees, the x value would be 81.3cm, this doesn't actually have to do with the fish's real position.

Is there something that I'm just not getting or am I just a small brain?
tms !8HZioZhw1c - Thu, 28 Apr 2022 22:13:53 EST 7A5arjSW No.80114 Reply
1651198433218.png -(11002B / 10.74KB, 501x426) Thumbnail displayed, click image for full size.
It's a practical matter. If you shift to get the proper angle for spearing the fish, the apparent position of the fish will also shift. Even if the fish itself stays perfectly still. As the diagram shows, the actual position of the fish isn't necessarily directly below its image. But you know it's somewhere along the line connecting the x position directly below the fish's image to the point on the water's surface you perceive the fish. So by spearing down through that surface point toward the position 31.3 cm below where you perceive the fish, you're guaranteed to spear the fish. Make sense?

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