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.
b) Calculate the actual depth of the trout
I have calcualted the angle of incidence to be 32 degrees, but still have no idea how to figure out the depth. I have been trying for 2 hours since last night. I don't know what trig to use on this. Can you help please?
physics - bobpursley, Saturday, January 16, 2010 at 10:30am
So Real depth= apparent depth/ tan i
check my thinking.
physics - drwls, Saturday, January 16, 2010 at 10:30am
The formula that you need is derived and presented here:
The object will appear at a shallower depth equal to the real depth divided by the refractive index of water.
physics - Sarah N H, Saturday, January 16, 2010 at 11:15am
Bob: your website, when I rearrange the formula, would be real depth = X/tani...What is the 'x" in my problem?
DRWLS: I am solving for the actual depth, the apparent depth is given...do I still use your same formula?
Thankyou both
physics - another question - Damon, Saturday, January 16, 2010 at 11:35am
Sarah,
Draw the figure three of us have suggested carefully labeling all the angles as is done in the links that Bob Pursley and Dr WLS have given you. r = 45. i =32 if that is what you got. Then you can work on the triangles and figure it out.
physics - another question - Sarah N H, Saturday, January 16, 2010 at 11:53am
I have drawn them all, but just want to make sure that I should be dividing 2 metres into tan1 (which is 32, to give me a real depth of 3 metres. Can you please verify that?
you should be dividing 2 by tan 32 giving 3.2 meters. The number of digits depends on how the original 2 meters was written.
To calculate the actual depth of the trout, you can use the formula:
Real depth = Apparent depth / tan(angle of incidence)
In this case, the apparent depth of the trout is given as 2.0m and the angle of incidence is 32 degrees. Plugging in these values into the formula:
Real depth = 2.0m / tan(32 degrees)
Now, you need to use a calculator to find the value of the tangent of 32 degrees, which is approximately 0.625. Dividing the apparent depth by this value:
Real depth = 2.0m / 0.625 ≈ 3.2m
So, the actual depth of the trout is approximately 3.2 meters.
To calculate the actual depth of the trout, you can use the formula Real depth = Apparent depth / tan(angle of incidence).
In this case, the apparent depth of the trout is given as 2.0m, and you have correctly determined the angle of incidence to be 32 degrees. So the formula becomes:
Real depth = 2.0m / tan(32 degrees)
To calculate this, you can either use a scientific calculator that has a tan function, or you can use a trigonometric table or online calculator.
Using the formula, you can determine that the real depth of the trout is approximately 3.13m.