Explanation:
A classic problem in optics!
Let's break it down step by step:
1. The angle of observation is 20° (θ1).
2. The horizontal distance from the incident light beam to the fish is 60 cm (d).
3. The refractive indices of air (n1) and water (n2) are given.
We can use Snell's law to relate the angles and refractive indices:
n1 sin(θ1) = n2 sin(θ2)
where θ2 is the angle of refraction in water.
First, we need to find the angle of refraction θ2:
θ2 = arcsin((n1 sin(θ1)) / n2)
θ2 ≈ 14.46° (using the given values)
Now, we can use the tangent function to relate the angles and distances:
tan(θ1) = d / T
tan(θ2) = d / Tfish
where T is the apparent depth (due to refraction) and Tfish is the actual depth.
Rearranging these equations, we get:
T = d / tan(θ1)
Tfish = d / tan(θ2)
Plugging in the values, we get:
T ≈ 34.64 cm (apparent depth)
Tfish ≈ 51.31 cm (actual depth)
So, due to refraction, you would underestimate the depth of the fish by about 16.67 cm (51.31 - 34.64).
