What is the critical angle of an air to glass interface if the refractive index of glass is 1.50.
The Correct Answer and Explanation is:
The critical angle of an air-to-glass interface can be calculated using Snell’s law, which relates the angle of incidence and the angle of refraction between two media. The critical angle occurs when the angle of refraction is 90°, meaning that the refracted light travels along the boundary of the two media (the interface). At this point, total internal reflection occurs, and no light is transmitted into the second medium.
The formula for the critical angle ((\theta_c)) is given by:
[
\sin(\theta_c) = \frac{n_2}{n_1}
]
Where:
- (n_1) is the refractive index of the first medium (air in this case).
- (n_2) is the refractive index of the second medium (glass in this case).
Given:
- The refractive index of air ((n_1)) is approximately 1.00.
- The refractive index of glass ((n_2)) is 1.50.
We can now substitute these values into the equation:
[
\sin(\theta_c) = \frac{1.00}{1.50} = 0.6667
]
To find the critical angle, we take the inverse sine (also known as arcsine) of 0.6667:
[
\theta_c = \sin^{-1}(0.6667) \approx 41.8^\circ
]
Thus, the critical angle for the air-to-glass interface is approximately 41.8°.
Explanation:
The critical angle depends on the refractive indices of both media involved. When light moves from a medium with a higher refractive index (glass) to a medium with a lower refractive index (air), the light is bent away from the normal. As the angle of incidence increases, there is a point at which the refracted ray lies along the boundary between the two media. This point is known as the critical angle, beyond which total internal reflection occurs, and no light exits into the air. Total internal reflection is used in fiber optics and other optical devices, where light is kept within the medium by repeatedly reflecting off the boundaries.