# Index of Refraction Concept - Extremely Confusing

I have just a few more questions regarding index of refractions and reflections...

8. A fly is 10 cm above the surface of a pond. How high above the water does the fly appear to a fish directly below (nair = 1, nwater = 1.333)?

(A) 10 cm
(B) 7.5 cm
(C) 13.3 cm
(D) 12.5 cm
(E) fish cannot see the fly because the light is totally reflected

The answer is supposed to be C but how did they figure this out?
They gave me height (h = 10 cm), but I have no angles of refraction, no just the index of refractions. But I have no formula to solve for HEIGHT because I can't use Snell's Law Equation. This makes no sense :(

9. What angle of incidence in degrees is sunlight 100% polarized when reflecting from the surface of the pond in the previous question?

(A) 0º
(B) 53º
(C) 37º
(D) 45º
(E) there is no angle

The answer is B, but how?

Is there a formula to use for them that I don't know about...
I've tried SNell's law but I'm not given enough variables.

wukunlin
Gold Member
for #8, you can see that the answer is the ratio of one index over another. The way you work this out (You don't need to do this every time after you understand the concept) is actually draw the fish and the fly and the water/air boundary. Draw some ray-tracing lines from the fish to the fly. You should be able to find that the perceived height and actual height lie on the same side of two similar triangles, which ratio simplifies to that of the refractive indices.

read up Brewster's angle on #9

For the first one, remember that the distance depends on the time it takes for light to reach the other object.

$c$ is the speed of light in a vacuum, but through a medium the speed of light is less. Since visually distance depends on time, you can find out the distance.

Second, the angle of polarization is the angle at which reflected light forms a right angle with the transmitted light. This is called Brewster's angle, and it's formula is: $\theta_{B} = arctan(\frac{n_{2}}{n_{1}})$

I hope this makes things clearer.