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Chapter 23: Problem 6

Light rays from the Sun, which is at an angle of \(35^{\circ}\) above the western horizon, strike the still surface of a pond. (a) What is the angle of incidence of the Sun's rays on the pond? (b) What is the angle of reflection of the rays that leave the pond surface? (c) In what direction and at what angle from the pond surface are the reflected rays traveling?

Short Answer

Expert verified
Answer: The angles of incidence and reflection are both \(55^{\circ}\), and the reflected rays are moving at a \(55^{\circ}\) angle from the pond surface in the opposite direction of the incident rays.

Step by step solution

01

(Step 1: Calculate the angle of incidence)

To find the angle of incidence, we will first find out how much of the given angle is above the surface level. Since the pond is a flat surface, the surface level is at 90掳 from the vertical. Thus, the angle of incidence of the Sun's rays on the pond surface can be calculated as follows: Angle of Incidence = 90掳 - Angle of Elevation of the Sun In the given exercise, the angle of elevation of the Sun is \(35^{\circ}\). Therefore, the angle of incidence is: Angle of Incidence = 90掳 - \(35^{\circ}\) = \(55^{\circ}\)
02

(Step 2: Determine the angle of reflection)

According to the laws of reflection, the angle of incidence equals the angle of reflection, which means if the incident angle is \(55^{\circ}\), then the angle of reflection will also be \(55^{\circ}\). Angle of Reflection = Angle of Incidence = \(55^{\circ}\)
03

(Step 3: Find the direction and angle of reflected rays)

Since the angle of reflection is equal to the angle of incidence, the reflected rays are traveling in a direction that forms an angle with the pond's surface equal to the angle of reflection. In this case, the angle is \(55^{\circ}\). Therefore, the reflected rays are moving at a \(55^{\circ}\) angle from the pond surface in the opposite direction of the incident rays. In summary, the angle of incidence is \(55^{\circ}\), the angle of reflection is \(55^{\circ}\), and the reflected rays are moving at a \(55^{\circ}\) angle from the pond surface in the opposite direction of the incident rays.

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