Homework Help: Refractive index and depth of object in water.

1. Mar 15, 2012

heartOFphysic

Question:
A Fsherman sees a Fish in a river at an apparent depth below the surface of
the water of 0.75 m. Given that the refractive index of water is 1.33, is the
true depth of the Fish below the water's surface:
A 0.75 m?
B Less than 0.75 m?
C 1 m?
D More than 1 m?

My proposal:

I am not really sure about this at all. All I can think of is "if the refractive index of water is 1.33 then the depth could be 1.33 times that of what it seems to be" (however I CAN'T prove this, it's just a hunch)

So 0.75 X 1.33 is roughly 1, so is the answer 1m?

2. Mar 15, 2012

Staff: Mentor

Draw a light ray from the fish and entering the eye of the observer. Make sure you show the correct way it bends as it passes from water into air.

3. Mar 15, 2012

PeterO

If you have ever looked into a swimming pool while the surface is smooth [you have to get there early before everyone jumps in] you would realise that the water appears different depths at different angle of observation.
Looking straight down it appears deepest - but even then shallower that it actually is.
I think I have seen somewhere that the apparent depth is 1/n times the real depth - referring to the apparent depth when looking directly into the medium - angle of incidence = 0 degrees.

4. Mar 15, 2012

tiny-tim

hi heartOFphysic!

yes, do as NascentOxygen suggests …
i'm a fish, and i know!

5. Mar 15, 2012

heartOFphysic

so it's (0.75)/ (1/1.333) = 0.99975

thus 1m?

6. Mar 16, 2012

Staff: Mentor

Can you work out the diagram (a vertical cross-section through the water) using the basic formula, Snell's Law? http://en.wikipedia.org/wiki/Refractive_index

That will be more useful to helping you understand what's involved here than guessing, and hoping for the best.

7. Mar 16, 2012

emailanmol

Hey,

This problem can be solved only for small angles.
Everyone above has pointed put some really useful tips.

The best way for you to start is to first derive a general formulae.(you will need a diagram.you can take help of text books because its not as simple as it sounds).
(Hint: You have some idea regarding the resulting formulae .Just go through the derivation again )

From there you will obtain a result which will be valid only for small angles of observation.
Plug in values and find the answer

8. Mar 16, 2012

tiny-tim

and small fish

9. Mar 16, 2012

emailanmol

Lol tiny-tim.

I have read many posts of yours and I got to admit,
'Not only are your posts to the point, they also tend to create an ambience of fun and happiness which helps the OP a lot'.

Cheers
Anmol