A fisherman in a stream 39 cm deep looks downward into the water and sees a rock on the stream bed. How deep does the stream appear to the fisherman

30cm

Explanation:

assume that the eyes are substantially above the water so that sin(theta) is approximately theta.

( small angle approximation).

The point at which a ray leaving the fish hits the surface of the water is x to the side of the centreline and the depth of the water is d

x/d = sin( angle of incidence)

if the apparent depth of the water is h then

x/h = sin( angle of refraction)

and applying snells law

1 sin ( theta air) = 1.33 sin( theta water)

1 * x/h = 1.33 * x/d

d/h = 1.33

or h/d = 1/1.33

h/39 = 1.33

h = 39 /1.33 so that is the apparent depth of the stream assuming:-

1. Your eyes are almost directly overhead

and

2. your eyes are a significant distance above the surface of the water.

x/d = 1.33 x/h

h/d =39/1.3

= 30cm

what experimental evidence led scientists to change from the previous model to this one?

a few of the positive particles aimed at a gold foil seemed to bounce back.

the colors of light emitted from heated atoms had very specific energies.

experiments with water vapor showed that elements combine in specific proportions.

cathode rays were bent in the same way whenever a magnet was brought near them.