A glass plate whose index of refraction is 1.47 is immersed in a liquid. The surface of the glass is inclined at an angle of 53.0° with the vertical. A horizontal ray in the glass is incident on the interface. When the liquid is a certain alcohol, the incident ray arrives at the interface at the critical angle. What is the index of refraction of the alcohol?
âsin53/sin 90 = n/n(gl)
n=n(gl) •sin53=1.47•0.8=1.17
To solve this problem, we can use the equation for the critical angle of refraction:
sin(critical angle) = 1 / index of refraction.
We are given that the glass plate has an index of refraction of 1.47, and the incident ray arrives at the interface at the critical angle. Let's denote the critical angle as θc.
sin(θc) = 1 / 1.47.
To find the index of refraction of the alcohol, we need to determine the angle of incidence when the incident ray arrives at the interface at the critical angle.
By Snell's Law, we know that
n1 * sin(θ1) = n2 * sin(θ2),
where n1 is the index of refraction of the medium the incident ray is coming from, θ1 is the angle of incidence, n2 is the index of refraction of the medium the incident ray is entering, and θ2 is the angle of refraction.
In this case, the incident ray is traveling from the glass (n1 = 1.47) to the alcohol (n2 = ?). The surface of the glass is inclined at an angle of 53.0° with the vertical, which means that the angle of incidence, θ1, is 90° - 53.0° = 37.0°.
Since the incident ray arrives at the interface at the critical angle, the angle of refraction, θ2, is 90°.
Therefore, we have:
1.47 * sin(37.0°) = n2 * sin(90°).
We can solve this equation to find the index of refraction of the alcohol, n2.
n2 = (1.47 * sin(37.0°)) / sin(90°).
Using a calculator, we can evaluate this expression:
n2 ≈ 1.00.
Therefore, the index of refraction of the alcohol is approximately 1.00.