What is the angle of refraction of a light ray that enters the surface of a calm lake from air at an angle of 45o to the normal? The refractive index of water is 1.333.
I don't even know how to start this or what the formula is. Thanks for your help in advance. It really is appreciated.
I got 32.1 degrees. The problem worked out should read
0.532=sin(theta)
sin-1 (0.532)=theta
32.1 degrees=theta
Snell's law:
n1 Sin(theta)=n2 Sin(thea)
Index of refraction of air (n1)=1.00
angle of incidence is 45 to the normal (sin theta)
Index of refraction of lake (n2)=1.33
solve for theta
Okay so then 1(sin45) = 1.33(sinx)
I got 32.04degrees?
n1 Sin(theta)=n2 Sin(theta)
Index of refraction of air (n1)=1.00
angle of incidence is 45 to the normal (sin theta)
Index of refraction of lake (n2)=1.33
solve for theta
(1.00/1.33)sin45=sin(theta)
0.544=sin(theta)
sin-1 (0.544)=theta
33.0 degrees=theta
Thank you so much
To find the angle of refraction, you can use Snell's Law, which relates the angle of incidence and the angle of refraction to the refractive indices of the two mediums. Snell's Law is given by:
n1 * sin(theta1) = n2 * sin(theta2)
where:
n1 and n2 are the refractive indices of the two mediums (in this case, air and water),
theta1 is the angle of incidence, and
theta2 is the angle of refraction.
In this case, the light ray is entering from air into water. The refractive index of air is approximately 1 (since it is close to a vacuum), and the refractive index of water is 1.333.
Given:
n1 = 1 (refractive index of air)
n2 = 1.333 (refractive index of water)
theta1 = 45 degrees (angle of incidence)
First, we need to convert the angle from degrees to radians since trigonometric functions in most programming languages typically operate with radians. The conversion is:
theta1_rad = theta1 * pi / 180
Now, we can plug the values into Snell's Law and solve for theta2.
1 * sin(theta1_rad) = 1.333 * sin(theta2)
To isolate theta2, divide both sides of the equation by 1.333:
sin(theta2) = (1/1.333) * sin(theta1_rad)
Now, take the inverse sine of both sides to find theta2:
theta2_rad = arcsin((1/1.333) * sin(theta1_rad))
To get the result in degrees, convert theta2_rad back to degrees:
theta2_deg = theta2_rad * 180 / pi
Now, substitute the values and perform the calculations:
theta1_rad = 45 * pi / 180
theta2_rad = arcsin((1/1.333) * sin(theta1_rad))
theta2_deg = theta2_rad * 180 / pi
Using these steps, you can find the angle of refraction.