A ray of light enters the top of a glass of water at an angle of 36 degrees with the vertical. What is the angle between the refracted ray and vertical?
The answer is 26 degrees but I keep getting 22 degrees.
I used snell's law: n1sinθ1=n2sinθ2
for n1 I thought it would be air: n=1.00
θ1=36 degrees
I thought n2 would be the water so n=1.33
and θ2 is what I am trying to find. When I plug everything in I get 22. So what am I doing wrong?
Am I using the wrong n values?
To solve this problem, you are correct to use Snell's law, which relates the angles of incidence and refraction to the indices of refraction for the two media involved.
Here's how you can correctly use Snell's law:
1. Identify the indices of refraction for the two media involved: air and water. The index of refraction for air is approximately 1.00, and for water, it is approximately 1.33. So your initial assumption was correct.
2. Determine the angle of incidence (θ1): You correctly identified the angle of incidence as 36 degrees with the vertical.
3. Plug the values into Snell's law equation:
n1 * sin(θ1) = n2 * sin(θ2)
n1 = 1.00
θ1 = 36 degrees
n2 = 1.33
1.00 * sin(36 degrees) = 1.33 * sin(θ2)
4. Rearrange the equation to solve for θ2:
sin(θ2) = (1.00 * sin(36 degrees)) / 1.33
θ2 = arcsin [(sin(36 degrees) * 1.00) / 1.33]
5. Calculate the value using a calculator:
θ2 ≈ 26 degrees
So, you have correctly used Snell's law, but it seems there may have been a calculation error. By recalculating, you should find that the angle between the refracted ray and the vertical is approximately 26 degrees, not 22 degrees.
Your approach to using Snell's law is correct, but there might be a mistake in your calculation. Let's go through the steps again to double-check.
Given:
n1 (refractive index of air) = 1.00
θ1 (angle of incidence) = 36 degrees
n2 (refractive index of water) = 1.33
θ2 (angle of refraction) = ?
Using Snell's law: n1sinθ1 = n2sinθ2
Substituting the values:
1.00 * sin(36) = 1.33 * sin(θ2)
To find θ2, divide both sides of the equation by 1.33:
sin(θ2) = (1.00 * sin(36)) / 1.33
Now, taking the inverse sine (arcsin) of both sides to find θ2:
θ2 = arcsin((1.00 * sin(36)) / 1.33)
Using a calculator, evaluate the right side of the equation to get the value of θ2. It should be approximately 26 degrees. If you are getting a different result, please check if you are using the correct units (radians vs. degrees) or if there is a rounding error in your calculations.
sin36=4/3 * sin Theta
sintheta= 3/4 * sin36=.4408
Theta(angle of refraction)=26deg, measured from the normal.