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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 48a
Chapter 34, Problem 48a

The 80-cm-tall, 65-cm-wide tank shown in FIGURE P34.48 is completely filled with water. The tank has marks every 10 cm along one wall, and the 0 cm mark is barely submerged. As you stand beside the opposite wall, your eye is level with the top of the water. Can you see the marks from the top of the tank (the 0 cm mark) going down, or from the bottom of the tank (the 80 cm mark) coming up? Explain.


Verified step by step guidance
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Step 1: Understand the problem setup. The tank is filled with water, and the observer's eye is level with the top of the water. The marks on the tank wall are spaced every 10 cm, starting from the 0 cm mark at the top (barely submerged) to the 80 cm mark at the bottom. The question asks whether the marks are visible from the top going down or from the bottom coming up.
Step 2: Recall the concept of refraction. Light bends when it passes from one medium to another due to the change in speed. In this case, light travels from water (higher refractive index) to air (lower refractive index). The bending of light depends on the angle of incidence and the refractive indices of the two media, governed by Snell's Law: n1sinθ=n2sinθ, where n1 and n2 are the refractive indices of water and air, respectively.
Step 3: Analyze the geometry of the tank and the observer's position. The observer is looking across the tank, and the light rays from the marks on the tank wall must refract at the water-air interface to reach the observer's eye. The critical angle for total internal reflection can be calculated using sin−1(n2n1), but here we focus on the qualitative behavior of light.
Step 4: Consider the path of light rays from the marks. Marks closer to the top of the tank (0 cm mark) will have light rays that refract at smaller angles, making them visible to the observer. As the observer looks deeper into the tank, the light rays from lower marks (closer to the 80 cm mark) will refract at larger angles. At some point, the angle may exceed the critical angle, causing total internal reflection, and these marks will no longer be visible.
Step 5: Conclude based on the physics of refraction. The observer will see the marks starting from the top of the tank (0 cm mark) going down. This is because the light rays from the upper marks refract at smaller angles and reach the observer's eye, while the marks deeper in the tank may become invisible due to total internal reflection or insufficient refraction to reach the observer.

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Key Concepts

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

Refraction of Light

Refraction is the bending of light as it passes from one medium to another, such as from air into water. This bending occurs because light travels at different speeds in different materials. In this scenario, the light rays from the marks in the tank will bend as they exit the water, affecting how they are perceived by the observer's eye.
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Line of Sight

The line of sight is the straight path along which an observer looks to see an object. In this case, the observer's eye is level with the top of the water, which influences which marks can be seen. The angle at which the observer looks at the marks will determine whether they can see the marks at the top or the bottom of the tank.
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Total Internal Reflection

Total internal reflection occurs when light attempts to move from a denser medium (like water) to a less dense medium (like air) at an angle greater than the critical angle. This phenomenon can prevent light from escaping the water, which may affect visibility of the marks at the bottom of the tank when viewed from above.
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Related Practice
Textbook Question

A 4.0-m-wide swimming pool is filled to the top. The bottom of the pool becomes completely shaded in the afternoon when the sun is 20° above the horizon. How deep is the pool?

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Textbook Question

The place you get your hair cut has two nearly parallel mirrors 5.0 m apart. As you sit in the chair, your head is 2.0 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

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Textbook Question

A light ray in air is incident on a transparent material whose index of refraction is n. Find an expression for the (non-zero) angle of incidence whose angle of refraction is half the angle of incidence.

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Textbook Question

A horizontal meter stick is centered at the bottom of a 3.0-m-deep, 3.0-m-wide pool of water. Suppose you place your eye just above the edge of the pool and look along the direction of the meter stick. What angle do you observe between the two ends of the meter stick if the pool is (a) empty and (b) completely filled with water?

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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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Textbook Question

A red ball is placed at point A in FIGURE P34.44. What are the (x, y) coordinates of each image?

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