a point source is on the bottom of a pool 2m deep. find the diameter of the largest circle at the surface which light can emerge from the water (n=1.33)

sinθ = 1/1.33

θ=48.7°
Now, the radius r is

r/2 = tanθ

To find the diameter of the largest circle at the surface through which light can emerge from the water, we can use Snell's Law. Snell's Law relates the angles of incidence and refraction of light as it passes through the interface between two different media.

Here are the steps to find the answer:

1. Determine the index of refraction of water (n₁) and the index of refraction of air (n₂).

In this case, the index of refraction of water is given as n=1.33 (n₁=1.33), and the index of refraction of air is approximately 1 (n₂=1).

2. Calculate the critical angle (θc) using the formula:

θc = arcsin(n₂/n₁)

Substituting the values, we have:

θc = arcsin(1/1.33)

Use a scientific calculator to find the value of θc.

3. Calculate the angle of incidence (θi) using the formula:

θi = 90° - θc

This will give us the maximum angle at which light can enter the water and still emerge at the surface.

4. Calculate the angle of refraction (θr) using Snell's Law, which states:

n₁ × sin(θi) = n₂ × sin(θr)

Substituting the values, we have:

1.33 × sin(θi) = 1 × sin(90°)

Simplify the equation by substituting sin(90°) with 1.

1.33 × sin(θi) = 1

Solve for sin(θi) and then calculate θi using an inverse sine function.

5. Calculate the length of the arc of the surface of the water (S) using the formula:

S = (2 × π × R × θi) / 360°

Here, R represents the radius of the circle at the surface.

6. Calculate the diameter (D) of the largest circle using:

D = 2 × R

Now, we can substitute the value of the radius obtained from the previous step into this equation to find the diameter.

By following these steps, you can find the diameter of the largest circle at the surface through which light can emerge from the water.