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Ch 34: Ray Optics
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
All textbooksKnight Calc 5th EditionCh 34: Ray OpticsProblem 55
Chapter 34, Problem 55

A horizontal laser beam enters the glass prism shown in FIGURE P34.55. When the laser beam exits the prism, by what angle will it have been deflected from horizontal?

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Identify the key concepts involved: refraction of light and Snell's Law. Refraction occurs when light passes from one medium to another, changing its speed and direction. Snell's Law is given by: n1⁢sin⁢θ1=n2⁢sin⁢θ2, where n is the refractive index and θ is the angle of incidence or refraction.
Determine the refractive indices of the two media involved. For example, the refractive index of air is approximately n=1.00, and the refractive index of the glass prism will be given or assumed (e.g., n=1.50).
Apply Snell's Law at the point where the laser beam enters the prism. Use the given angle of incidence (or assume it if not provided) to calculate the angle of refraction inside the prism. Rearrange Snell's Law to solve for the angle of refraction: θ2=sin⁢⁢-1⁢(n1⁢sin⁢θ1n2).
Trace the path of the laser beam through the prism. At the second interface (where the beam exits the prism), apply Snell's Law again to calculate the angle of refraction as the beam exits back into the air. Use the angle of incidence at this interface and the refractive indices of the glass and air.
Calculate the total deflection angle. The deflection angle is the difference between the initial direction of the laser beam (horizontal) and its final direction after exiting the prism. Use geometry to determine this angle based on the angles of refraction and the geometry of the prism.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Refraction

Refraction is the bending of light as it passes from one medium to another, caused by a change in its speed. When light enters a denser medium, like glass from air, it slows down and bends towards the normal line. Conversely, when it exits back into a less dense medium, it speeds up and bends away from the normal. This principle is crucial for understanding how the laser beam behaves as it travels through the prism.
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Index of Refraction

Snell's Law

Snell's Law quantitatively describes the relationship between the angles of incidence and refraction when light passes between two media with different refractive indices. It is expressed as n1 * sin(θ1) = n2 * sin(θ2), where n is the refractive index and θ is the angle relative to the normal. This law is essential for calculating the angles at which the laser beam enters and exits the prism, allowing us to determine the total deflection.
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Snell's Law

Total Internal Reflection

Total internal reflection occurs when a light ray attempts to move from a denser medium to a less dense medium at an angle greater than the critical angle, resulting in the light being completely reflected back into the denser medium. While this phenomenon is not directly applicable to the exit of the laser beam from the prism, understanding it helps clarify the behavior of light at the boundaries of different media, which is important for analyzing the overall path of the beam.
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Related Practice
Textbook Question

There's one angle of incidence β onto a prism for which the light inside an isosceles prism travels parallel to the base and emerges at angle β. A laboratory measurement finds that β=52.2° for a prism shaped like an equilateral triangle. What is the prism's index of refraction?

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Textbook Question

Shown from above in FIGURE P34.54 is one corner of a rectangular box filled with water. A laser beam starts 10 cm from side A of the container and enters the water at position x. You can ignore the thin walls of the container. If x = 15 cm, does the laser beam refract back into the air through side B or reflect from side B back into the water? Determine the angle of refraction or reflection.

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Textbook Question

Shown from above in FIGURE P34.54 is one corner of a rectangular box filled with water. A laser beam starts 10 cm from side A of the container and enters the water at position x. You can ignore the thin walls of the container. Find the minimum value of x for which the laser beam passes through side B and emerges into the air.

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Textbook Question

You're visiting the shark tank at the aquarium when you see a 2.5-m-long shark that appears to be swimming straight toward you at 2.0 m/s. What is the shark's actual speed through the water? You can ignore the glass wall of the tank.

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Textbook Question

Optical engineers need to know the cone of acceptance of an optical fiber. This is the maximum angle that an entering light ray can make with the axis of the fiber if it is to be guided down the fiber. What is the cone of acceptance of an optical fiber for which the index of refraction of the core is 1.55 while that of the cladding is 1.45? You can model the fiber as a cylinder with a flat entrance face.

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Textbook Question

An astronaut is exploring an unknown planet when she accidentally drops an oxygen canister into a 1.50-m-deep pool filled with an unknown liquid. Although she dropped the canister 21 cm from the edge, it appears to be 31 cm away when she peers in from the edge. What is the liquid's index of refraction? Assume that the planet's atmosphere is similar to earth's.

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