using Snell's Law (sin(theta1)/sin(theta2) = v1/v2 where (theta1) is the angle of incidence and (theta2) is the angle of refration. The number V1/V2 is called the index of refraction. The index of refraction from air to water is 4/3. If a ray of light passes through the surface of a lake at an angle of incidence of 70 degrees what is the angle of refraction?

Question

using Snell's Law (sin(theta1)/sin(theta2) = v1/v2 where (theta1) is the angle of incidence and (theta2) is the angle of refration. The number V1/V2 is called the index of refraction. The index of refraction from air to water is 4/3. If a ray of light passes through the surface of a lake at an angle of incidence of 70 degrees what is the angle of refraction?

Answer 1

To find the angle of refraction using Snell's Law, we need the angle of incidence and the index of refraction.

Given:
Angle of incidence, theta1 = 70 degrees
Index of refraction from air to water, v1/v2 = 4/3

Step 1: Convert the angle of incidence from degrees to radians.
The formula for converting degrees to radians is: radians = degrees * (pi/180)
So, theta1 in radians = 70 * (pi/180)

Step 2: Apply Snell's Law: sin(theta1) / sin(theta2) = v1 / v2
Rearranging the formula, sin(theta2) = (v2 / v1) * sin(theta1)

Step 3: Substitute the given values:
Substituting theta1 = 70 * (pi/180) and v1/v2 = 4/3, we get:
sin(theta2) = (4/3) * sin(70 * pi/180)

Step 4: Calculate the angle of refraction.
Take the inverse sine (sin^-1) of both sides to solve for theta2.
theta2 = sin^-1((4/3) * sin(70 * pi/180))

Using a calculator, evaluate the right-hand side to find the angle of refraction. The result will be in radians. If you want the value in degrees, you can convert it by multiplying by (180/pi).

Please note that in this specific case, the calculation involves both pi and trigonometric functions (sine). The use of a scientific calculator or a programming language that supports trigonometry will be helpful.