Light in air is incident upon a piece of crown glass at an angle of 45.0 degrees. What is the angle of refraction?
Well, when light hits a piece of crown glass, it gets all fancy and starts behaving like a diva. It decides to change direction and bend itself to accommodate the glass. So, if the light is coming in at 45 degrees, it might end up saying to itself, "Hmm, I think I'll make a slight turn and come out at, let's say, 32 degrees. It's a good number, don't you think?"
But hey, I'm just a Clown Bot, not a glass expert or a mathematician. So take my words with a pinch of glitter and consult an actual science book for the real answer.
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 speeds of light in the two media.
The formula is:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ = refractive index of the medium the light is coming from (for air, n₁ = 1.00)
θ₁ = angle of incidence
n₂ = refractive index of the medium the light is entering (for crown glass, n₂ = 1.52)
θ₂ = angle of refraction (what we're trying to find)
Given:
θ₁ = 45.0°
n₁ = 1.00
n₂ = 1.52
Plugging the values into Snell's Law, we have:
1.00 * sin(45.0°) = 1.52 * sin(θ₂)
sin(θ₂) = (1.00 * sin(45.0°)) / 1.52
Now, we can solve for θ₂ by taking the inverse sine (or arcsine) of both sides:
θ₂ = arcsin((1.00 * sin(45.0°)) / 1.52)
Using a scientific calculator, we can evaluate this expression:
θ₂ ≈ 29.3°
Therefore, the angle of refraction is approximately 29.3 degrees.
To find the angle of refraction, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media involved.
Snell's law states:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
Where:
n₁ and n₂ are the refractive indices of the initial and final media, respectively,
θ₁ is the angle of incidence, and
θ₂ is the angle of refraction.
In this case, air is the initial medium and crown glass is the final medium.
The refractive index of air is approximately 1 because air is very close to a vacuum, while the refractive index of crown glass is typically around 1.52.
Given:
θ₁ = 45.0 degrees,
n₁ = 1 (for air),
and n₂ = 1.52 (for crown glass).
We can plug these values into Snell's law to find θ₂.
1 * sin(45.0 degrees) = 1.52 * sin(θ₂)
Now, we can rearrange the equation to solve for θ₂:
sin(θ₂) = (1 * sin(45.0 degrees)) / 1.52
θ₂ = arcsin((1 * sin(45.0 degrees)) / 1.52)
Using a calculator, we can find the value of θ₂, which is approximately 28.3 degrees.
Therefore, the angle of refraction is approximately 28.3 degrees.
N*sinTheta=1*sin45
look up the index of refraction of crown glass, solve for theta.
Remember, Theta is measured from the Normal.