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Chapter 23: Problem 24

Is there a critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium that has an index of refraction \(1.4 ?\) If so, what is the critical angle that allows total internal reflection in the first medium?

Short Answer

Expert verified
If so, what is the value of the critical angle? Answer: No, there is no critical angle in this case, as total internal reflection is not possible when the light ray travels from a medium with a lower index of refraction (1.2) to a medium with a higher index of refraction (1.4).

Step by step solution

01

Understand the concept of critical angle

The critical angle is the angle of incidence above which the light ray undergoes total internal reflection within the first medium. This phenomenon occurs when the angle of refraction equals 90 degrees, and the light ray travels along the interface between the two media without entering the second medium.
02

Apply Snell's Law

To find the critical angle, we can use Snell's Law, which is given by: $$n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(\theta_2)$$ where \(n_1\) and \(n_2\) are the indices of refraction of the first and second media, and \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction, respectively.
03

Determine if there is a critical angle

In the case of total internal reflection, the angle of refraction \(\theta_2\) becomes 90 degrees. Therefore, Snell's Law can be rewritten as: $$n_1 \cdot \sin(\theta_1) = n_2 \cdot \sin(90^{\circ})$$ Since the sine of 90 degrees equals 1, the equation simplifies to: $$n_1 \cdot \sin(\theta_1) = n_2$$ Total internal reflection can only occur if the light is traveling from a medium with a higher index of refraction to a medium with a lower index of refraction. In this exercise, \(n_1 = 1.2\) and \(n_2 = 1.4\). Since \(n_1 < n_2\), total internal reflection is not possible, and there is no critical angle in this case.
04

Summary

In conclusion, there is no critical angle for a light ray coming from a medium with an index of refraction 1.2 and incident on a medium with an index of refraction 1.4, as total internal reflection is not possible in this scenario.

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