An underwater scuba diver sees the Sun at an apparent angle of 34.0° from the vertical. What is actual direction of the Sun? ° (above the horizon)
Refraction of Light
Refraction is a change in the direction of light rays when they travel from one medium to another. It is the bending of light when it goes through different media.
Angle of Refraction
Light is considered by many scientists to have dual nature, both particle nature and wave nature. First, Particle nature is one in which we consider a stream of packets of energy called photons. Second, Wave nature is considering light as electromagnetic radiation whereas part of it is perceived by humans. Visible spectrum defined by humans lies in a range of 400 to 700 nm wavelengths.
Index of Refraction of Diamond
Diamond, the world’s hardest naturally occurring material and mineral known, is a solid form of the element carbon. The atoms are arranged in a crystal structure called diamond cubic. They exist in a huge variety of colours. Also, they are one of the best conductors of heat and have a very high melting point.
![**Problem Statement:**
An underwater scuba diver sees the Sun at an apparent angle of 34.0° from the vertical. What is the actual direction of the Sun?
**Solution:**
To calculate the actual direction of the Sun, one must consider Snell's Law, which describes how light refracts between different media. The apparent angle given is from the vertical underwater. To find the angle above the horizon, refraction at the water-air boundary must be accounted for. Typically, this involves using the indices of refraction for water and air.
**(Explanation of Factors):**
- **Apparent angle (34.0°)**: This is the angle measured from the vertical underwater.
- **Vertical Line**: The reference from which the apparent angle is measured.
To solve, you would utilize Snell's Law:
\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \]
where \( n_1 \) and \( n_2 \) are the refractive indices of the two media (water and air, respectively), and \( \theta_1 \) and \( \theta_2 \) are the angles from the normal.
**Calculation Example:**
If assuming:
- Index of Refraction for water (\( n_1 \)): 1.33
- Index of Refraction for air (\( n_2 \)): 1.00
This problem requires calculating the real angle of the Sun (\( \theta_2 \)) using the formula, understanding that the angle to be found is with respect to the horizontal above water.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4889a1b2-cd02-493f-a3b5-7c3cbfe1f622%2F1d7944e4-0cc2-4b0d-b5e8-43bc37771285%2Fr3uo77pu_processed.jpeg&w=3840&q=75)
Step by step
Solved in 4 steps
