Why Does an Object's Apparent Depth Change in Water?

[app]

INTRODUCTION: I am having problems solving Some Optics MCQs recently.
THE PROBLEMS : (1) T is a point at the bottom of a tank filled with water, as shown in the diagram. The refractive index of water is 4/3.YPT is the vertical line through T.To an observer at the position O, T will appear to be:(multiple options may be correct)
(i)To the left of YT.
(ii)Somewhere on YT.
(iii)At a depth 3m below T.
(iv)At a depth <3m below T.
DIAGRAM IN WORDS: In case the diagram is not visible, the point O is directly above the right edge of the tank and the point T is somewhere at the middle of the bottom of the tank.
WHAT I KNOW: The position of the apparent image will change with the angle of viewing. So, we can leave out option (ii). I think option (i) has to be correct.
WHAT I CANNOT UNDERSTAND: But I'm can't make out what options (iii) and (iv) really want to say. Which of them is correct (if at all)? And why? I really don't understand why an image will be formed "below" T? We are viewing it from a rarer medium and the point T is in water (denser medium). Then why is the term "below T" give in the options (iii) and (iv)?
CONCLUSION: I know i shouldn't have posted so many questions all at a time, but any help will be appreciated. Thanks a lot.

 

[Andrew Mason]

INTRODUCTION: I am having problems solving Some Optics MCQs recently.
THE PROBLEMS : (1) T is a point at the bottom of a tank filled with water, as shown in the diagram. The refractive index of water is 4/3.YPT is the vertical line through T.To an observer at the position O, T will appear to be:(multiple options may be correct)
(i)To the left of YT.
(ii)Somewhere on YT.
(iii)At a depth 3m below T.
(iv)At a depth <3m below T.
DIAGRAM IN WORDS: In case the diagram is not visible, the point O is directly above the right edge of the tank and the point T is somewhere at the middle of the bottom of the tank.
WHAT I KNOW: The position of the apparent image will change with the angle of viewing. So, we can leave out option (ii). I think option (i) has to be correct.
WHAT I CANNOT UNDERSTAND: But I'm can't make out what options (iii) and (iv) really want to say. Which of them is correct (if at all)? And why? I really don't understand why an image will be formed "below" T? We are viewing it from a rarer medium and the point T is in water (denser medium). Then why is the term "below T" give in the options (iii) and (iv)?
CONCLUSION: I know i shouldn't have posted so many questions all at a time, but any help will be appreciated. Thanks a lot.

Think of the light rays coming from the object at T and reaching the eye at O. When the light rays from T reach the water-air boundary, a direction change occurs. Does the ray bend toward or away from a line perpendicular to the surface? Now the eye/brain thinks the light travels in a straight line from the object (extend the light ray that reaches O past the surface). Where does the object appear to the observer in relation to the actual position of the object at T?

AM

 

[app]

I want to know something else...

Does the ray bend toward or away from a line perpendicular to the surface?

WHAT I KNOW: I know that water is optically denser than air. So, obviously the rays from T will bend away from the normal (perpendicular) at the water-air interface. That is not my question.
WHAT I WANT TO KNOW: I cannot understand the meaning of options (iii) and (iv). They are talking about the apparent image to be at a distance 3m below T. But my question is : "How is it possible that the apparent image will be formed "BELOW" T?" It is obviously not going to be formed below T, that's for sure.
WHAT MY BOOK SAYS: My book says that option (iv) (At a depth <3m below T)
is correct. I want to know how? Thanks.

 

[Andrew Mason]

WHAT I KNOW: I know that water is optically denser than air. So, obviously the rays from T will bend away from the normal (perpendicular) at the water-air interface. That is not my question.
WHAT I WANT TO KNOW: I cannot understand the meaning of options (iii) and (iv). They are talking about the apparent image to be at a distance 3m below T. But my question is : "How is it possible that the apparent image will be formed "BELOW" T?" It is obviously not going to be formed below T, that's for sure.
WHAT MY BOOK SAYS: My book says that option (iv) (At a depth <3m below T)
is correct. I want to know how? Thanks.

Read the rest of my first response!

Extend the rays from the object that reach O backward to the point where they intersect. That point is where in relation to the point of intersection with YPT and is the location that the brain sees the object (which is at T)? Is that above or below T? Is it to the left or right of T?

You ask how it is possible that an image would be formed below T. It depends on how the light ray bends at the surface. If the light ray bent toward the normal (instead of away from the normal as in this case), where would the image of the object appear to be?

AM

 

[app]

I do know about bending of light rays at surfaces, and when and how or how much, etc. if we look from a medium which is denser than water, then obviously the opposite of what happens here will take place.That is the image will be formed below T. But the thing is that my book says that option (iv) given along with the question is correct. I just want to know how option (iv) is correct. All that u have said is correct and i have understood that.Thanks for helping. But please please just let me know why option (iv) i.e. the last option is correct. I know that in this case the image will obviously be formed above T as i have shown in the diagram. And of course, thanks a lot for helping out.

 

[Andrew Mason]

I do know about bending of light rays at surfaces, and when and how or how much, etc. if we look from a medium which is denser than water, then obviously the opposite of what happens here will take place.That is the image will be formed below T. But the thing is that my book says that option (iv) given along with the question is correct. I just want to know how option (iv) is correct. All that u have said is correct and i have understood that.Thanks for helping. But please please just let me know why option (iv) i.e. the last option is correct. I know that in this case the image will obviously be formed above T as i have shown in the diagram. And of course, thanks a lot for helping out.

There seems to be something missing from the question because there is no mention of a distance of 3m. I assumed that was the depth of the object at below the surface. Give us the entire problem in the exact original wording and we will try to help you figure it out.

AM

 

[app]

That Is Exactly What The Question Says...

Thats exactly what the question says , word for word. I have already given the whole question. But maybe there is a misprint in the book. Anyway, can u please tell me what change would occur if the observer O is not near the edge but looking from a point almost above T (but not exactly vertically above T, since then the image will be formed on the line joining T and O (ithink so). Thanks for helping out.

 

[Andrew Mason]

Thats exactly what the question says , word for word. I have already given the whole question. But maybe there is a misprint in the book.

Then I have no idea where the 3m comes from. Is there a previous related question with some reference to distances?

Anyway, can u please tell me what change would occur if the observer O is not near the edge but looking from a point almost above T (but not exactly vertically above T, since then the image will be formed on the line joining T and O (ithink so). Thanks for helping out.

It would appear to be directly below the observer (ie on the line). But the object would look bigger than it is because the light from the edges of the object would bend away from the normal slightly toward the observer's eye.

AM

 

[app]

Then I have no idea where the 3m comes from. Is there a previous related question with some reference to distances?

It would appear to be directly below the observer (ie on the line). But the object would look bigger than it is because the light from the edges of the object would bend away from the normal slightly toward the observer's eye.

AM

But let's say we consider a point object and neglect the increase in size. But now if we look at that point object from a place above water and in between the edge and the vertical line through the object, then where will the object be? I know its confusing but that's the best way i can explain in a physics forum. Do you get me? See, i have done quite a number of optics problems but there whenever we were considering the formation of image , we assumed it to be on the vertical line through the object. Let's say, for example, while deriving that relation of apparent depth, real depth and the refractive index of the medium.All that mattered was the depth from the surface and nothing else. But now i got a problem (that wrong one with that God-knows-where-from-3metre problem) and in this problem, an observer is looking from the edge. Very good, let him look from the edge if he wants to (its his wish). But now i find that the apparent image will no longer be formed on the vertical line but will be formed somewhere left or right of the vertical line, depending on from which edge he wishes to see. But now i want to ask, that if he looks from somewhere in between the edge and vertical line, then where will the apparent image be formed.
SUMMARY:-
IF VIEWED FROM A POINT VERTICALLY ABOVE THE OBJECT- Apparant image formed somewhere on the vertical line.
IF VIEWED FROM THE EDGE- Apparant image formed at a point left or right of the vertical line, depending on from which edge he wishes to see.
IF VIEWED FROM A POINT IN BETWEEN THE TWO POINTS MENTIONED ABOVE- Apparant image formed at __________________? (Please fill in the blank)

I'm really really confused, please help and thanks a lot.

 

[Andrew Mason]

But let's say we consider a point object and neglect the increase in size. But now if we look at that point object from a place above water and in between the edge and the vertical line through the object, then where will the object be? I know its confusing but that's the best way i can explain in a physics forum. Do you get me? See, i have done quite a number of optics problems but there whenever we were considering the formation of image , we assumed it to be on the vertical line through the object.

It is really a matter of perception. The brain thinks it is closer if it appears bigger and further away if it appears smaller.

Put the eye directly above the object. Give the object some width and draw the light rays from the objects edges to the surface and then to the eye. Extend them back through the water. Those extended rays provide the image the eye sees. Then move the eye horizontally. As the eye moves, the spread of those extended rays increases and moves closer to the surface. So the object will appear to be higher and closer than it was when directly above it.

AM