Question

A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of $\theta_a = 36.2{^\circ}$, the ray refracted into the water makes an angle of 49.8$^\circ$ with the normal to the interface. What is the smallest value of the incident angle $\theta_a$ for which none of the ray refracts into the water?

Name: Problem 16, Chapter 33: University Physics with Modern Physics
Uploaded: 2019-08-07T15:53:05-08:00
Duration: 1 min 4 s
Channel: Salamat Ali

   A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of $\theta_a = 36.2{^\circ}$, the ray refracted into the water makes an angle of 49.8$^\circ$ with the normal to the interface. What is the smallest value of the incident angle $\theta_a$ for which none of the ray refracts into the water?

University Physics with Modern Physics

Hugh D. Young 14th Edition

Chapter 33, Problem 16

Instant Answer

Solved by Expert Salamat Ali

08/07/2019

Step 1

In this case, the two media are glass and water. The formula for Snell's law is: $$n_1 \sin(\theta_1) = n_2 \sin(\theta_2)$$ where $n_1$ and $n_2$ are the indices of refraction for the two media, and $\theta_1$ and $\theta_2$ are the angles of incidence and Show more…

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A flat piece of glass covers the top of a vertical cylinder that is completely filled with water. If a ray of light traveling in the glass is incident on the interface with the water at an angle of $\theta_a = 36.2{^\circ}$, the ray refracted into the water makes an angle of 49.8$^\circ$ with the normal to the interface. What is the smallest value of the incident angle $\theta_a$ for which none of the ray refracts into the water?

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Key Concepts

Snell’s Law

Snell's Law is a fundamental principle in optics that relates the angles of incidence and refraction to the refractive indices of two media. It states that the product of the refractive index of the first medium and the sine of the angle of incidence is equal to the product of the refractive index of the second medium and the sine of the angle of refraction. This law is used to describe how light bends when it passes from one medium to another through an interface.

Critical Angle and Total Internal Reflection

The critical angle is the angle of incidence in the higher-index medium beyond which no refraction occurs, and all the light is reflected back into that medium. When light strikes the interface at an angle greater than the critical angle, total internal reflection occurs. This concept is derived from Snell's Law by setting the angle of refraction to 90° in the lower-index medium, resulting in a formula for the critical angle.

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