To find the angle of refraction, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the speed of light in the first medium to the speed of light in the second medium.
Let's denote the angle of incidence as θ₁ and the angle of refraction as θ₂.
The speed of light in air is approximately equal to the speed of light in vacuum, so we can assume it to be the same for our calculation.
The speed of light in water is about 3/4 times the speed of light in air, so the ratio of the speed of light in the first medium to the speed of light in the second medium is 1/3/4 = 4/3.
Snell's Law can be written as follows:
sin(θ₁)/sin(θ₂) = 4/3
We are given that the angle of incidence is 55°, so let's substitute θ₁ = 55°:
sin(55°)/sin(θ₂) = 4/3
To find θ₂, we can rearrange the equation:
sin(θ₂) = sin(55°) * (3/4)
sin(θ₂) = (0.8192) * (3/4)
sin(θ₂) = 0.6144
To find the angle of refraction, we take the inverse sine of both sides:
θ₂ = sin^(-1)(0.6144)
θ₂ ≈ 38.7°
Therefore, the angle of refraction is approximately 38.7°.
The critical angle for water is the angle of incidence at which the refracted ray is parallel to the surface of the water. This occurs when the angle of refraction is 90°.
Using Snell's Law, we can find the critical angle by substituting θ₂ = 90° and solving for θ₁:
sin(θ₁)/sin(90°) = 4/3
sin(θ₁) = (4/3) * 1
sin(θ₁) = 4/3
To find the critical angle, we take the inverse sine of both sides:
θ₁ = sin^(-1)(4/3)
Using a calculator, we find that θ₁ ≈ 75.5°.
Therefore, the critical angle for water is approximately 75.5°.
A ray of light passes from air into water at an angle to the surface of the the water of 55°. Find the angle of refraction and the critical is the water
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