Someone on a glass-bottom boat shines a light through the glass into the water below. A scuba diver beneath that boat sees the light at an angle of 17 degrees with resoect to the normal. If the glass's index of refraction is 1.5 and the water's index of refraction 1.33, what is the angle of incidence with which the light passes from the glass into the water?

40.53

To solve this problem, we can use Snell's law, which relates the angles of incidence and refraction to the indices of refraction of the two media involved. Snell's law states:

n₁ * sin(θ₁) = n₂ * sin(θ₂)

Where:
- n₁ and n₂ are the indices of refraction of the first and second media, respectively.
- θ₁ and θ₂ are the angles of incidence and refraction, respectively, measured with respect to the normal.

Let’s denote the angle of incidence with respect to the normal as θ₁ and the angle of refraction with respect to the normal as θ₂.

Given data:
- Index of refraction of the glass (first medium) = 1.5
- Index of refraction of the water (second medium) = 1.33
- Angle of refraction (θ₂) = 17 degrees

We need to find the angle of incidence (θ₁).

Rearranging Snell's law, we get:

sin(θ₁) = (n₂ / n₁) * sin(θ₂)

Now we can substitute the values:

sin(θ₁) = (1.33 / 1.5) * sin(17°)

Calculating:

sin(θ₁) = 0.88 * 0.2924

sin(θ₁) ≈ 0.257

To find the angle θ₁, we take the inverse sine (also known as arcsine) of 0.257:

θ₁ ≈ arcsin(0.257)

Using a calculator, we find:

θ₁ ≈ 15.14 degrees

Therefore, the angle of incidence with which the light passes from the glass into the water is approximately 15.14 degrees.