A light ray in air strikes the surface of a lake at an angle of incidence of 46 degrees. What is the angle of refraction in the water?
Snell's Law says that
1.0* sin I = N*sin R
Use water's index of refraction N to calculate the angle R.
Look up the index of refraction. It is about 1.33
n=air =1.00) nH20=1.33)
To find the angle of refraction in the water, we can use Snell's Law, which relates the angle of incidence and the angle of refraction when light passes from one medium to another. Snell's Law is given by:
n₁ * sin(θ₁) = n₂ * sin(θ₂),
where:
- n₁ and n₂ are the refractive indices of the two media (in this case, air and water),
- θ₁ is the angle of incidence,
- θ₂ is the angle of refraction.
In this case, the light is passing from air to water. The refractive index of air (n₁) is approximately 1, and the refractive index of water (n₂) is approximately 1.33.
We are given that the angle of incidence (θ₁) is 46 degrees.
Substituting the values into Snell's Law, we have:
1 * sin(46°) = 1.33 * sin(θ₂).
Now, we can solve for θ₂. Rearranging the equation:
sin(θ₂) = (1 * sin(46°)) / 1.33.
Taking the inverse sine (sin⁻¹) of both sides, we get:
θ₂ = sin⁻¹((1 * sin(46°)) / 1.33).
Evaluating this expression using a calculator, we find that the angle of refraction in the water (θ₂) is approximately 33.25 degrees.