Sam is sitting in her fishing boat watching a trout swim below the surface. She guesses the apparent depth of the trout at 2.0m. She estimates that her eyes are about 1.0 m above the water's surface, and that the angle at which she's observing the trout is 45 degrees.

a) draw a diagram t show the ACTUAL depth of the trout and the path of light from the trout to Sam's eyes
b) Calculate the actual depth of the trout

You have to remember that in the air, the light from the fish is bent away from the normal.

See Snell's law. Use your diagram to calculate the depth, using trig.

Bob - thanks for the reply. I have figured out the angle of incidence to be 32.3 degrees, but do not know how to caluclate the depth as underwater heigh is given (the only heigh is 1 m above water which I don't think i useful)...can you please help me more.

* I meant, NO underwater height is given

It says "it looks" like the fish is 2 meters deep.

Draw a straight line from the eye to the water, hitting at 45 degrees.
Continue the straight line (ignoring Snell's Law below the water until it is 2 meters under.
Now go back and do the correct angle in the water from the point where the line hit the water.
The fish is on that line and a vertical line through the point where it "looked like" the fish was.

I figured out the angle to be 32 degrees but still don't know how to figure out the height...

a) To draw the diagram, you can start by drawing a horizontal line across the page to represent the surface of the water. Label this line as "Water Surface." Then, draw a vertical line from the water surface to represent the depth of the trout. Label this line as "Actual Depth of Trout." The length of this line will be the actual depth of the trout.

Next, label a point on the water surface as "Sam's Eyes." Draw a straight line from this point to the top of the vertical line. This line represents the path of light from the trout to Sam's eyes. Since Sam estimates that her eyes are 1.0m above the water's surface, make sure this line is inclined upward at an angle to indicate this.

Lastly, label the angle formed between the vertical line representing the depth of the trout and the path of light from the trout to Sam's eyes. This angle is given as 45 degrees.

b) To calculate the actual depth of the trout, we can use trigonometry. In this case, we can use the tangent function.

Tangent of an angle (θ) is equal to the opposite side (O) divided by the adjacent side (A). In this case, the opposite side is the actual depth of the trout, and the adjacent side is the distance from Sam's eyes to the top of the water's surface.

The tangent of 45 degrees is equal to 1. We know that the angle is 45 degrees and the adjacent side is 1.0m, so we can set up the equation:

tan(45°) = Actual Depth of Trout / 1.0m

Since tan(45°) = 1, we can simplify the equation to:

1 = Actual Depth of Trout / 1.0m

Solving for the Actual Depth of Trout, we find:

Actual Depth of Trout = 1.0m

Therefore, the actual depth of the trout is 1.0 meters.