Questions: Calculate the critical angle when light travels from a medium (n=2.4) to air?

Solution Steps

The critical angle is the angle of incidence in the denser medium (with a higher refractive index) at which the angle of refraction in the less dense medium (with a lower refractive index) is 90 degrees. This occurs when light travels from a medium with a higher refractive index to one with a lower refractive index.

Snell's Law relates the angles and refractive indices of the two media: $$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$ where $n_1$ is the refractive index of the first medium (2.4), $\theta_1$ is the angle of incidence, $n_2$ is the refractive index of the second medium (air, which is approximately 1.0), and $\theta_2$ is the angle of refraction.

For the critical angle, the angle of refraction $\theta_2$ is 90 degrees. Therefore, $\sin(\theta_2) = \sin(90^\circ) = 1$.

Substitute the known values into Snell's Law: $$2.4 \sin(\theta_c) = 1 \cdot 1$$ $$\sin(\theta_c) = \frac{1}{2.4}$$ $$\theta_c = \arcsin\left(\frac{1}{2.4}\right)$$

Using a calculator, find the arcsine: $$\theta_c \approx \arcsin(0.4167) \approx 24.62^\circ$$

Final Answer