The angle of incidence when the angle between the incident ray and refracted ray is 80 degrees is......
To find the angle of incidence when the angle between the incident ray and refracted ray is 80 degrees, we need to use Snell's Law. Snell's Law 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 speeds of light in the two mediums.
Mathematically, Snell's Law can be written as:
sin(θ₁) / sin(θ₂) = v₁ / v₂
Where:
θ₁ = Angle of incidence
θ₂ = Angle of refraction
v₁ = Speed of light in the first medium
v₂ = Speed of light in the second medium
In this case, we know the angle between the incident ray and refracted ray is 80 degrees. Let's assume the angle of incidence is θ₁ and the angle of refraction is θ₂.
Given: θ₂ - θ₁ = 80 degrees
We can rearrange Snell's Law as:
sin(θ₁) = (v₁ / v₂) * sin(θ₂)
Next, since we don't know the values of v₁ and v₂ or the angle of refraction θ₂, we cannot find the exact value of the angle of incidence θ₁. However, we can use an example to demonstrate how to find the angle of incidence for a specific scenario.
Let's say the incident ray is traveling from air (v₁ ≈ 3 x 10^8 m/s) to water (v₂ ≈ 2.25 x 10^8 m/s), and the angle of refraction θ₂ is 40 degrees. Using this information, we can calculate the angle of incidence θ₁.
sin(θ₁) = (v₁ / v₂) * sin(θ₂)
sin(θ₁) = (3 x 10^8 / 2.25 x 10^8) * sin(40)
Now, use a calculator to evaluate the right side of the equation and find the sine inverse to determine θ₁.
θ₁ ≈ sin^(-1) [(3 x 10^8 / 2.25 x 10^8) * sin(40)]
The resulting angle will be the angle of incidence for this specific scenario. Remember to always specify the values of v₁, v₂, and θ₂ to calculate the angle of incidence in a practical situation.