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Chapter 11: Problem 27

A light ray strikes the core of an fiber-optic cable at 30 angle of incidence, If the critical angel of the core is \(15^{\circ}\), will the light ray be reflected or reflected?

Short Answer

Expert verified
Since the angle of incidence (30掳) is greater than the critical angle (15掳), the light ray will undergo total internal reflection and remain inside the fiber-optic cable. Therefore, the light ray will be reflected.

Step by step solution

01

Recall Snell's Law and the total internal reflection concept

Snell's Law relates the angles of incidence to the refractive indices of the two materials in contact. The formula for Snell's Law is: \(n_1 \sin{\theta_1} = n_2 \sin{\theta_2}\) Here, - \(n_1\) and \(n_2\) are the refractive indices of two different materials, - \(\theta_1\) is the angle of incidence, - \(\theta_2\) is the angle of refraction. Total internal reflection is a phenomenon in which a light ray undergoes reflection instead of transmission when it hits a boundary between one medium and another. This happens when the angle of incidence is greater than the critical angle.
02

Determine the critical angle

We are given the critical angle for the core of the fiber-optic cable, which is 15掳. Therefore: \(critical \;angle = 15^{\circ}\)
03

Compare the angle of incidence to the critical angle

We have to determine whether the light ray will be transmitted or reflected. This depends on whether the angle of incidence is greater than, less than, or equal to the critical angle. The angle of incidence is given as 30掳. Since the angle of incidence (30掳) is greater than the critical angle (15掳): \(30^{\circ} > 15^{\circ}\)
04

Conclude whether the light ray is transmitted or reflected

Since the angle of incidence (30掳) is greater than the critical angle (15掳), the light ray will undergo total internal reflection and remain inside the fiber-optic cable. Thus, the light ray will be reflected.

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