Solve Light Refraction Homework: Angle of Sunlight in Water

In summary, an underwater swimmer observed a beam of sunlight in the water at an angle of 18.7° with the vertical. The index of refraction for water is 1.33. To determine the beam's angle as it enters the water, the equation n1sin(theta1)=n2sin(theta2) can be used. After a few attempts, the correct angle was found by taking the angle of 18.7° as the angle after it entered the water, leading to the realization that the initial angle must be calculated as 90-18.7=71.3°.
  • #1
JDiorio
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Homework Statement


An underwater swimmer observes that a beam of sunlight in the water makes an angle of 18.7° with the vertical. The index of refraction for water is equal to 1.33. Assuming the surface of the water is level, determine the beam's angle as it enters the water.


Homework Equations



n1sin(theta1)=n2sin(theta2)


The Attempt at a Solution



I tried using different angles but I can't seem to get the correct answer. At first I used 18.7 degrees and found that to be incorrect. Than I thought that 18.7 might not correspond since it is made with the vertical and not the horizontal, so I used 90-18.7= 71.3 degrees but that didnt work either. I am not sure if I am using the wrong equation or if I am misreading the question.
 
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  • #2
Nevermind I found my mistake. I didn't realize the 18.7 degree angle was after it already was in the water. Thanks anyway.
 
  • #3


As a scientist, it is important to carefully read and analyze the given information and equations before attempting to solve a problem. In this case, the given information is the angle of sunlight in water (18.7°) and the index of refraction for water (1.33). The equation provided is the Snell's law, which relates the angles and indices of refraction of light as it passes through different mediums.

To solve this problem, we can use the given information and the Snell's law to determine the angle of sunlight as it enters the water. Let's label the angles and indices of refraction as follows:

n1 = index of refraction of air (assumed to be 1 since it is not specified)
n2 = index of refraction of water (given as 1.33)
θ1 = angle of incidence (unknown)
θ2 = angle of refraction (given as 18.7°)

Using the Snell's law, we can write:

n1sinθ1 = n2sinθ2

Substituting the given values, we get:

1sinθ1 = (1.33)sin18.7°

Solving for θ1, we get:

θ1 = sin^-1 (1.33sin18.7°)

θ1 = 29.1°

Therefore, the angle of sunlight as it enters the water is 29.1°. This is the angle measured from the horizontal, since the angle of 18.7° is measured from the vertical.

It is important to note that the angle of refraction (θ2) is always measured from the normal (perpendicular) to the surface of the water, while the angle of incidence (θ1) can be measured from any reference line. In this case, we chose to measure it from the horizontal.

In summary, the correct approach to solving this problem involves correctly identifying and labeling the given information and using the appropriate equation (Snell's law) to solve for the unknown angle. Additionally, it is important to pay attention to the units (degrees or radians) and reference lines when working with angles in physics problems.
 

1. What is light refraction?

Light refraction is the bending of light rays as they pass from one medium to another with a different optical density. It occurs because the speed of light changes when it moves from one medium to another, causing it to change direction.

2. How does light refraction affect the angle of sunlight in water?

When sunlight passes from air to water, it slows down and changes direction due to light refraction. This causes the angle of the sunlight to decrease as it enters the water, making it appear to bend.

3. What is the angle of sunlight in water?

The angle of sunlight in water is the angle between the incoming ray of sunlight and the surface of the water. It is determined by the angle of incidence (the angle between the incoming ray and a line perpendicular to the surface) and the refractive index of water.

4. How is the angle of sunlight in water calculated?

The angle of sunlight in water can be calculated using Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media. This can be represented as n1sinθ1 = n2sinθ2, where n1 is the refractive index of air, θ1 is the angle of incidence, n2 is the refractive index of water, and θ2 is the angle of refraction.

5. What factors can affect the angle of sunlight in water?

The angle of sunlight in water can be affected by the refractive index of water, the angle of incidence, and the wavelength of light. It can also be affected by external factors such as the depth of the water and the surface conditions, such as waves or turbulence.

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