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?
http://www.saburchill.com/physics/chapters3/0004.html
So Real depth= apparent depth/ tan i
check my thinking.
The formula that you need is derived and presented here:
http://www.physicstutorials.org/index.php/home/optics/refraction-of-light/apparent-depth-real-depth
The object will appear at a shallower depth equal to the real depth divided by the refractive index of water.
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.
Of course, I can help you with that! To find the actual depth of the trout, we can use the concept of trigonometry.
Let's first understand the problem and the given information. We have the apparent depth of the trout from Sam's perspective, which is 2.0m. Sam estimates that her eyes are about 1.0m above the water's surface, and she's observing the trout at an angle of 45 degrees.
To find the actual depth of the trout, we can use the tangent function (tan) from trigonometry. The formula we will use is:
tan(angle of incidence) = actual depth / apparent depth
In this case, the angle of incidence is the angle between Sam's line of sight and a line perpendicular to the water's surface. We'll refer to this angle as 'x'. And the apparent depth is given as 2.0m.
Let's substitute the known values into the formula and solve for the actual depth:
tan(x) = actual depth / 2.0
Now, in order to find the angle 'x', we can use the fact that the sum of the angles of any triangle is 180 degrees.
We have two known angles: the angle at which Sam is observing the trout (45 degrees) and the angle formed by Sam's line of sight, the perpendicular to the water's surface, and the horizontal surface of the water (90 degrees).
To find 'x', we can subtract the sum of these two known angles from 180 degrees:
x = 180 - 45 - 90
x = 45 degrees
Now we can substitute the value of 'x' into our equation and solve for the actual depth:
tan(45) = actual depth / 2.0
Using the value of tan(45) (which is 1), we can simplify the equation:
1 = actual depth / 2.0
Now we can solve for the actual depth:
actual depth = 1 * 2.0
actual depth = 2.0m
Therefore, the actual depth of the trout is 2.0 meters.
I hope this explanation helps you solve the problem! Let me know if you have any further questions.