Calculate the critical angle between flint glass and air assuming that index of refraction of the glass is 1.61.
To calculate the critical angle between flint glass and air, we need to use Snell's Law and the concept of the critical angle.
Snell's Law states:
n1 * sin(θ1) = n2 * sin(θ2)
where:
- n1 is the refractive index of the first medium (in this case, air)
- θ1 is the angle of incidence of the light ray in the first medium
- n2 is the refractive index of the second medium (in this case, flint glass)
- θ2 is the angle of refraction of the light ray in the second medium
For the critical angle, the angle of refraction (θ2) is equal to 90 degrees, meaning the light ray travels along the boundary between the two mediums. This occurs when the angle of incidence (θ1) is the critical angle (θc).
To find the critical angle, we need to rearrange Snell's Law as follows:
sin(θc) = n2 / n1
Substituting the given values:
n1 (air) = 1 (approximating the refractive index of air as 1)
n2 (flint glass) = 1.61
sin(θc) = 1.61 / 1
sin(θc) = 1.61
To find the critical angle, we need to take the inverse sine (sin⁻¹) of 1.61:
θc = sin⁻¹(1.61)
Using a scientific calculator, we find:
θc ≈ 63.65 degrees
Therefore, the critical angle between flint glass and air is approximately 63.65 degrees.