Solve Light Refraction Homework: Angle of Sunlight in Water

[JDiorio]

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.

 

[JDiorio]

Nevermind I found my mistake. I didn't realize the 18.7 degree angle was after it already was in the water. Thanks anyway.

 

[kerimek]

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.