Optimizing Dolphin Tracking: Calculating the Angle for Dart Gun Accuracy

[Seneka]

Homework Statement

A scientist investigating the movements of dolphins in the Mediterranean uses a dart gun to shoot small, harmless tracking devices onto the fins of dolphins. When standing on deck, her hand is 1m above the water, and looking along the dart gun she is holding at an angle of 45∘, she sees a dolphin. Using sonar she has found that the dolphin is swimming at a depth of 2m. We know that the refractive index for water is 1.33. At what angle from the horizontal should she point the dart gun to hit the dolphin?

Homework Equations

n1sintheta1=n2sintheta2
Answer:

The Attempt at a Solution

I worked out the angle in the water to be 32 degrees using the equation above and extended that line from the dolphin to the refracted ray above the water to the scientists hand. I knew that this would make an angle of 180 degrees so I subtracted 32 and 90 from 180 to give me 58 degrees as the answer. This is wrong but I don't understand why. Why do you treat the the two rays as vectors and why do you add them? What is wrong with my working out?

 

[haruspex]

and extended that line from the dolphin to the refracted ray above the water to the scientists hand.

That sequence does not produce a straight line, it merely reproduces the bent line in the ray diagram.
The task is to find the angle of the straight path the dart will take.

 

[Seneka]

That sequence does not produce a straight line, it merely reproduces the bent line in the ray diagram.
The task is to find the angle of the straight path the dart will take.

Cool, thanks

 

[Orodruin]

This problem seems very unrealistic and completely ignores whether or not that dart would actually be able to reach the dolphin after impacting on the water surface ...