An underwater scuba diver sees the sun at an apparent angle of 45 degrees from the vertical. What is the actual angle of the sun?
i don't know how to get the answer but the book says its 19.5 degrees can anyone help me?
Snells law is pretty clear. The answer that they give is the angle to the horizon, not to the normal. The Suns angle to the vertical is 70.5 degrees
The index of refraction of water is 1.33.
Use Snell's law.
1.33 sin 45 = sin X
The angle X that you get will be greater than 45 degrees, but they probably want the angle above the horizon for the sun, which would be the complement of X
20 degrees
Certainly! To find the actual angle of the sun, we can use the concept of refraction. Refraction occurs when light passes through different mediums, such as air and water, causing the light rays to bend.
In this scenario, when the scuba diver observes the sun underwater, the light from the sun passes through the air, water, and then enters the diver's eyes. The change in the speed of light in these different mediums causes the light rays to bend.
To determine the actual angle of the sun, we need to consider the relationship between the apparent angle observed by the diver and the refractive index, which is the ratio of the speed of light in air to the speed of light in water.
The refractive index of water is approximately 1.33. Here's how we can calculate the actual angle of the sun:
1. Convert the apparent angle from degrees to radians. Since the problem states an apparent angle of 45 degrees, this is equal to 45 * (π/180) radians.
2. Apply Snell's law, which relates the angles and refractive indices of light passing through different media:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ = refractive index of the medium the light is coming from (air)
n₂ = refractive index of the medium the light is entering (water)
θ₁ = angle of incidence (apparent angle)
θ₂ = angle of refraction (actual angle)
Considering that the refractive index of air is approximately 1, and the refractive index of water is 1.33, we can rearrange the equation to solve for θ₂:
sin(θ₂) = (n₁ / n₂) * sin(θ₁)
Plugging in the values:
sin(θ₂) = (1 / 1.33) * sin(apparent angle)
3. Now, calculate the actual angle of the sun by taking the inverse sine of sin(θ₂):
actual angle = arcsin(sin(θ₂))
Plugging in the values, we get:
actual angle = arcsin((1 / 1.33) * sin(apparent angle))
actual angle = arcsin((1 / 1.33) * sin(45 * (π/180)))
4. Calculate the actual angle by converting back to degrees:
actual angle in degrees = actual angle * (180/π)
Plugging in the values, we get:
actual angle in degrees ≈ arcsin((1 / 1.33) * sin(45 * (π/180))) * (180/π)
After performing the calculations, you'll find that the actual angle of the sun is approximately 19.5 degrees.