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

Transcript text: Calculate the critical angle when light travels from a medium $(\mathrm{n}=2.4)$ to air?

Solution

Solution Steps

Step 1: Understand the Concept of Critical Angle

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.

Step 2: Apply Snell's Law

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.

Step 3: Set the Angle of Refraction to 90 Degrees

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

Step 4: Solve for the Critical Angle

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

Step 5: Calculate the Critical Angle

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