The angle of refraction of a ray of light traveling through a piece of flint glass is 24°. Find the angle of incidence.
n1 sin T1 = n2 sin T2
n1 = 1.000
n2 = 1.655
1.000 sin T1 = 1.655 sin 24
sin T1 = .673
T1 = 42.3 degrees
The critical angle of refraction for ray of light passing from flint glass to air is
To find the angle of incidence, we can use Snell's law, which relates the angle of incidence (θ₁), the angle of refraction (θ₂), and the indices of refraction of the two mediums involved (n₁ and n₂). Snell's law states:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
In this case, we are given the angle of refraction (θ₂ = 24°) and we need to find the angle of incidence (θ₁). We also need to know the refractive index of flint glass (n₂), which is approximately 1.66.
Rearranging the equation, we have:
sin(θ₁) = (n₂ / n₁) * sin(θ₂)
Now, we can plug in the known values:
sin(θ₁) = (1.66 / n₁) * sin(24°)
To solve for θ₁, we can take the inverse sine (also known as arcsine) of both sides of the equation:
θ₁ = arcsin((1.66 / n₁) * sin(24°))
Note that the value of n₁, the refractive index of the initial medium (usually air), is approximately 1.
Therefore, to find the angle of incidence (θ₁) for a ray of light traveling through a piece of flint glass, the equation becomes:
θ₁ = arcsin((1.66 / 1) * sin(24°))