If in the previous problem, medium 1 is glass and medium 2 is air, which is a possible trajectory for the light beam? (A) \(\mathrm{A}\) (B) \(\mathrm{B}\) (C) \(\mathrm{C}\) (D) \(\mathrm{D}\) (E) \(\mathrm{E}\)

Short Answer

Expert verified
Answer: A, C, or E.

Step by step solution

01

Review Snell's law

To solve this problem, we need to use Snell's law, which states that the ratio between the sine of the angle of incidence (the angle between the incident ray and the normal) and the sine of the angle of refraction (the angle between the refracted ray and the normal) is constant. In this case, Snell's law will be written as: $$\frac{\sin \theta_1}{\sin \theta_2} = \frac{n_2}{n_1}$$ Where \(\theta_1\) and \(\theta_2\) are the angles of incidence and refraction, respectively, and \(n_1\) and \(n_2\) are the refractive indices of medium 1 (glass) and medium 2 (air), respectively. Remember that when light travels from a denser medium (higher refractive index) to a less dense medium (lower refractive index), the angle of refraction is larger than the angle of incidence.
02

Analyze trajectories based on the angle of refraction

We need to analyze each of the given trajectory options (A, B, C, D, and E) to determine which one corresponds to the light beam traveling from glass to air. Using Snell's law and considering that glass has a higher refractive index than air, the light will bend away from the normal when it enters the air. Therefore, the angle of refraction will be larger than the angle of incidence. Analyze each option and compare the angles: (A) The trajectory A shows light bending away from the normal when entering air, increasing the angle of refraction. (B) The trajectory B shows light bending towards the normal when entering air, decreasing the angle of refraction. (C) The trajectory C shows light bending away from the normal when entering air, increasing the angle of refraction. (D) The trajectory D shows light bending towards the normal when entering air, decreasing the angle of refraction. (E) The trajectory E shows light bending away from the normal when entering air, increasing the angle of refraction.
03

Identify the correct trajectory

As we analyzed in the previous step, trajectories A, C, and E show an increase in the angle of refraction, which is the correct behavior when light travels from a denser medium (glass) to a less dense medium (air). Therefore, the possible trajectory for the light beam is one of the options A, C, or E (but not B or D). Without further information or a diagram showing angles or other factors, we cannot determine which exact option out of A, C, or E is the correct one.

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