How Deep Does the Penny Appear in a Layered Liquid Tank?

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In summary, a lens is a curved piece of glass or plastic that can bend and focus light, used in various optical instruments such as cameras and microscopes. It works by refracting light to create a clear and magnified image. There are two main types of lenses, convex and concave, which bend light in different ways. Convex lenses converge light to form a real image, while concave lenses diverge light to create a virtual image. Lenses are used in everyday objects like eyeglasses and cameras, as well as in scientific and medical applications.
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Laxman2974
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Homework Statement



A 15-mm-thick layer of water (n = 1.33) floats on a 60-mm-thick layer of carbon tetrachloride (n = 1.46) in a tank. A penny lies at the bottom of the tank. At what depth below the top water surface do you perceive the penny? (Hint: Use the result and assumptions of Problem 21 and work with a ray diagram of the situation.)

How do I get started? DO I find the focal length?
 
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Have you tried following the hint? Please post what you have attempted so far.
 
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To begin, we can use Snell's law to determine the angle of refraction for light passing from water into carbon tetrachloride. We can then use this angle to construct a ray diagram and determine the apparent position of the penny. The focal length is not necessary for this problem, as we are not dealing with a lens but rather a change in medium. We can also assume that the light rays travel in a straight line and that the water and carbon tetrachloride layers are flat and parallel. From there, we can use basic trigonometry to calculate the depth at which the penny appears to be located. It is important to keep in mind the different refractive indices of the two layers and how they affect the path of the light rays. I hope this helps you get started on solving the problem.
 

Related to How Deep Does the Penny Appear in a Layered Liquid Tank?

1. What is a lens?

A lens is a curved piece of glass or plastic that can bend and focus light, used in various optical instruments such as cameras and microscopes.

2. How does a lens work?

A lens works by refracting (bending) light as it passes through, causing the light rays to converge or diverge. This allows the lens to focus an image on a specific point, creating a clear and magnified view of an object.

3. What are the types of lenses?

There are two main types of lenses: convex lenses and concave lenses. Convex lenses are thicker in the center and thinner at the edges, and they converge light rays to form a real image. Concave lenses are thinner in the center and thicker at the edges, and they diverge light rays to create a virtual image.

4. What is the difference between a convex and a concave lens?

The main difference between convex and concave lenses is the way they bend light. Convex lenses bend light rays towards a central point, while concave lenses cause light rays to spread out. This difference in bending results in different types of images being formed by the two types of lenses.

5. How are lenses used in everyday life?

Lenses are used in many everyday objects, such as eyeglasses, cameras, and telescopes. They are also used in scientific instruments like microscopes and telescopes to magnify and study small or distant objects. Lenses are also used in various industrial and medical applications, such as laser surgery and barcode scanners.

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