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Chapter 13: Problem 31

When swimming underwater, why is your vision made much clearer by wearing goggles with flat pieces of glass that trap air behind them? [Hint: You can simplify your reasoning by considering the special case where you are looking at an object far away, and along the optic axis of the eye.]

Short Answer

Expert verified
Goggles trap air, maintaining normal refraction at the air-cornea interface, allowing clear vision underwater.

Step by step solution

01

Understanding Light Refraction

When light travels from one medium to another (like from water to air), it bends or refracts. This bending occurs because light changes speed when it passes from one medium to another. In the case of the human eye underwater, light refracts at the water-cornea interface, which is different from the typical air-cornea interface. This significant change in refraction affects our ability to focus clearly on objects underwater.
02

Concept of Air-Water Interface

When not wearing goggles underwater, the light refracts directly from water to the cornea, altering the refraction angle, which makes it difficult for the eye to focus properly. This results in a blurred vision because the lens of the eye cannot adequately accommodate the refractive difference without the air interface.
03

Function of Goggles

Goggles create an artificial air pocket in front of the eyes. The flat glass or plastic pieces service to maintain an air layer just like above water. This traps air between the glass and the eye, maintaining the normal air-cornea interface, allowing the light to enter the eye the same way it does above water, thereby making vision clearer.
04

Refraction at the Air-Glass Interface

Light entering the goggles first refracts at the air-glass interface and then moves through the air before reaching the eye. This setup ensures that light refracts correctly at the two interfaces (glass-air and then air-cornea) without the complications of water refraction, allowing the eye to focus properly on distant objects.
05

Comparison Example

Think about looking at an object while above water versus underwater without goggles. In air, the focus is sharp due to the air-cornea interface, while underwater without goggles, this is lost. Goggles essentially restore this interface through the trapped air, making the underwater image clear as it would be above water.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Air-Water Interface
When swimming underwater, your eyes encounter an air-water interface issue. This interface is where two different mediums meet: air and water. Normally, light travels from air into your eye. The eye is designed to focus light that is refracted (or bent) mainly by the cornea-air interface.
However, when you are underwater without protection, light instead travels from water directly to the cornea. The change in medium affects how light bends when entering your eye. Water, being denser than air, alters the bending angle of the light more drastically.
  • The cornea cannot adjust enough to compensate for this change in light refraction.
  • This results in blurry, unfocused images underwater.
Understanding this concept helps you see why goggles are so beneficial when swimming.
Function of Goggles
Goggles are clever tools that solve the issue of poor underwater vision by maintaining the natural air-cornea interface. Essentially, when you wear goggles, they trap an air pocket right in front of your cornea. The flat lenses of the goggles, made of glass or plastic, seal off your eyes from direct water contact.
The air trapped between your eyes and the goggles mimicks the situation above water, allowing light to reach your eye in the same manner as outside the water. This trapped air helps in maintaining the normal focus and sharpen the image again.
  • This adjustment allows your eye to focus effectively, just as it would above water.
  • Goggles thus restore clarity and sharpness to your vision while swimming.
Refraction at the Air-Glass Interface
The function of goggles hinges on refraction at the air-glass interface. When light first contacts the goggle lens, it bends slightly due to the transition from air to glass. This refraction at the air-glass interface is quite controlled and predictable, unlike the drastic bending at the water-cornea interface.
Once light passes through the lens, it again travels through air until it reaches your eye.
  • This dual-interface setup of glass-air and air-cornea ensures that light refracts predictably and efficiently.
  • The goggle lens facilitates proper image focusing, maintaining a clear view under the water as you would have outside.
Optics in Vision Correction
Understanding optics and how they correct vision is key to understanding goggles' functions. Optics involves studying light's behavior as it interacts with various surfaces or mediums. In everyday life, eyeglasses are a common example of optics in vision correction, adjusting the focal length for clear, sharp vision.
Underwater, goggles similarly act as corrective lenses, even though you're not fixing a typical vision issue like nearsightedness or farsightedness.
  • They compensate for the refractive difference caused by water.
  • This optical adjustment allows light to enter your eyes in a way that enables you to see clearly under water.
Thus, the goggle creates an ideal condition for vision, owing to the precise refraction they provide.

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Most popular questions from this chapter

Based on Snell's law, explain why rays of light passing through the edges of a converging lens are bent more than rays passing through parts closer to the center. It might seem like it should be the other way around, since the rays at the edge pass through less glass - - - shouldn't they be affected less? In your answer: \- Include a ray diagram showing a huge, full-page, close-up view of the relevant part of the lens. \- Make use of the fact that the front and back surfaces aren't always parallel; a lens in which the front and back surfaces are always parallel doesn't focus light at all, so if your explanation doesn't make use of this fact, your argument must be incorrect. \- Make sure your argument still works even if the rays don't come in parallel to the axis.

Suppose a converging lens is constructed of a type of plastic whose index of refraction is less than that of water. How will the lens's behavior be different if it is placed underwater?

When ultrasound is used for medical imaging, the frequency may be as high as 5-20 MHz. Another medical application of ultrasound is for therapeutic heating of tissues inside the body; here, the frequency is typically \(1-3 \mathrm{MHz}\). What fundamental physical reasons could you suggest for the use of higher frequencies for imaging?

The figure shows a device for constructing a realistic optical illusion. Two mirrors of equal focal length are put against each other with their silvered surfaces facing inward. A small object placed in the bottom of the cavity will have its image projected in the air above. The way it works is that the top mirror produces a virtual image, and the bottom mirror then creates a real image of the virtual image. (a) Show that if the image is to be positioned as shown, at the mouth of the cavity, then the focal length of the mirrors is related to the dimension \(h\) via the equation $$\frac{1}{f}=\frac{1}{h}+\frac{1}{h+\left(\frac{1}{h}-\frac{1}{f}\right)^{-1}}$$ (b) Restate the equation in terms of a single variable \(x=h / f\), and show that there are two solutions for \(x\). Which solution is physically consistent with the assumptions of the calculation?

Fred's eyes are able to focus on things as close as \(5.0 \mathrm{~cm}\). Fred holds a magnifying glass with a focal length of \(3.0 \mathrm{~cm}\) at a height of \(2.0 \mathrm{~cm}\) above a flatworm. (a) Locate the image, and find the magnification. (b) Without the magnifying glass, from what distance would Fred want to view the flatworm to see its details as well as possible? With the magnifying glass? (c) Compute the angular magnification.
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