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# when light propagates from a material with a given index of refraction into a material with a smaller index of refraction, the speed of the light

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## The Law of Refraction

### LEARNING OBJECTIVE

By the end of this section, you will be able to:

Determine the index of refraction, given the speed of light in a medium.

It is easy to notice some odd things when looking into a fish tank. For example, you may see the same fish appearing to be in two different places. (See Figure 1.) This is because light coming from the fish to us changes direction when it leaves the tank, and in this case, it can travel two different paths to get to our eyes. The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction. Refraction is responsible for a tremendous range of optical phenomena, from the action of lenses to voice transmission through optical fibers.

### REFRACTION

The changing of a light ray’s direction (loosely called bending) when it passes through variations in matter is called refraction.

### SPEED OF LIGHT

The speed of light c not only affects refraction, it is one of the central concepts of Einstein’s theory of relativity. As the accuracy of the measurements of the speed of light were improved, c was found not to depend on the velocity of the source or the observer. However, the speed of light does vary in a precise manner with the material it traverses. These facts have far-reaching implications, as we will see in the chapter Special Relativity. It makes connections between space and time and alters our expectations that all observers measure the same time for the same event, for example. The speed of light is so important that its value in a vacuum is one of the most fundamental constants in nature as well as being one of the four fundamental SI units. Figure 1. Looking at the fish tank as shown, we can see the same fish in two different locations, because light changes directions when it passes from water to air. In this case, the light can reach the observer by two different paths, and so the fish seems to be in two different places. This bending of light is called refraction and is responsible for many optical phenomena.

Why does light change direction when passing from one material (medium) to another? It is because light changes speed when going from one material to another. So before we study the law of refraction, it is useful to discuss the speed of light and how it varies in different media.

## The Speed of Light

Early attempts to measure the speed of light, such as those made by Galileo, determined that light moved extremely fast, perhaps instantaneously. The first real evidence that light traveled at a finite speed came from the Danish astronomer Ole Roemer in the late 17th century. Roemer had noted that the average orbital period of one of Jupiter’s moons, as measured from Earth, varied depending on whether Earth was moving toward or away from Jupiter. He correctly concluded that the apparent change in period was due to the change in distance between Earth and Jupiter and the time it took light to travel this distance. From his 1676 data, a value of the speed of light was calculated to be 2.26 × 108 m/s (only 25% different from today’s accepted value). In more recent times, physicists have measured the speed of light in numerous ways and with increasing accuracy. One particularly direct method, used in 1887 by the American physicist Albert Michelson (1852–1931), is illustrated in Figure 2. Light reflected from a rotating set of mirrors was reflected from a stationary mirror 35 km away and returned to the rotating mirrors. The time for the light to travel can be determined by how fast the mirrors must rotate for the light to be returned to the observer’s eye. Figure 2. A schematic of early apparatus used by Michelson and others to determine the speed of light. As the mirrors rotate, the reflected ray is only briefly directed at the stationary mirror. The returning ray will be reflected into the observer’s eye only if the next mirror has rotated into the correct position just as the ray returns. By measuring the correct rotation rate, the time for the round trip can be measured and the speed of light calculated. Michelson’s calculated value of the speed of light was only 0.04% different from the value used today.

The speed of light is now known to great precision. In fact, the speed of light in a vacuum c is so important that it is accepted as one of the basic physical quantities and has the fixed value c = 2.9972458 × 108 m/s ≈ 3.00 × 108 m/s, where the approximate value of 3.00 × 108 m/s is used whenever three-digit accuracy is sufficient. The speed of light through matter is less than it is in a vacuum, because light interacts with atoms in a material. The speed of light depends strongly on the type of material, since its interaction with different atoms, crystal lattices, and other substructures varies. We define the index of refraction n of a material to be

n = c v n=cv

, where v is the observed speed of light in the material. Since the speed of light is always less than c in matter and equals c only in a vacuum, the index of refraction is always greater than or equal to one.

Source : courses.lumenlearning.com

## Physics Exam 4 Flashcards

Start studying Physics Exam 4. Learn vocabulary, terms, and more with flashcards, games, and other study tools.

## Physics Exam 4

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When moonlight strikes the surface of a calm lake, what happens to this light?

All of it enters the water.

Some of it reflects back to the air; some enters the water.

All of it reflects from the water surface back to the air.

All of it disappears via absorption by water molecules.

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Some of it reflects back to the air and some of it enters the water

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When the reflection of an object is seen in a flat mirror, the image is

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Virtual and upright

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1/42 Created by Bridget_Kiernan2

### Terms in this set (42)

When moonlight strikes the surface of a calm lake, what happens to this light?

All of it enters the water.

Some of it reflects back to the air; some enters the water.

All of it reflects from the water surface back to the air.

All of it disappears via absorption by water molecules.

Some of it reflects back to the air and some of it enters the water

When the reflection of an object is seen in a flat mirror, the image is

Virtual and upright

You want to create a spotlight that will shine a bright beam of light with all of the light rays parallel to each other. You have a large concave spherical mirror and a small lightbulb. Where should you place the lightbulb?

at the focal point of the mirror

When light propagates from a material with a given index of refraction into a material with a smaller index of refraction, the speed of the light

increases

What is the minimum value that the index of refraction can have?

+1

Now consider a ray of light that propagates from water (n=1.33) to air (n=1). If the incident ray strikes the water-air interface at an angle θ1≠0, which of the following relations regarding the angle of refraction, θ2, is correct?

theta 2 is greater than theta1

Consider a ray of light that propagates from water (n=1.33) to glass (n=1.52). If the incident ray strikes the water-glass interface at an angle θ1≠0, which of the following relations regarding the angle of refraction θ2 is correct?

Theta 2 is less than theta 1

Consider a ray of light that propagates from air (n=1) to any one of the materials listed below. Assuming that the ray strikes the interface with any of the listed materials always at the same angle θ1, in which material will the direction of propagation of the ray change the most due to refraction?

ice (n=1.309) water (n=1.333)

turpentine (n=1.472)

glass (n=1.523) diamond (n=2.417) Diamond (n=2.417)

In the case of n1>n2, if the incidence angle is increased, the angle of refraction

increases up to a max value of 90 degrees

If you shine a light through an optical fiber, why does it come out the end but not out the sides?

Total internal reflection makes the light reflect from the sides

A lens produces a real image of a real object. Is the image inverted or upright? Is the lens diverging or converging? is the image enlarged or reduced in size?

inverted converging

Cannot be determined

If two convex lenses identical in size and shape are manufactured from glass with two different indices of refraction, would the focal length of the lens with the greater index of refraction (lens 1) be larger or smaller than that of the other lens (lens 2)?

Smaller

If lens 1 from Part D were placed in exactly the same location as lens 2, would the image produced by lens 1 be larger or smaller than the image produced by lens 2?

Smaller

Sunlight is observed to focus at a point 16.5 cm behind a lens. What kind of lens is it?

Converging lens

To a swimmer under water, objects look blurry. When goggles are worn, however, the images are sharp. Why is this so?

The swimmer's eyes are adapted to refraction that takes place as light passes from the air into the cornea. The goggles maintain this.

To hit a fish that he sees beneath the water, where should he aim the bow?

Below the fish

A converging lens, such as a typical magnifying glass,

always produces an image smaller than the object.

always produces a magnified image (taller than object).

always produces an inverted image (upside down).

always produces an upright image.

None of these statements are true.

None of these statements are true

Virtual images can be formed by

plane and curved mirrors and lenses

You cover half of a lens that is forming an image on a screen. Compare what happens when you cover the top half of the lens versus the bottom half.

The image becomes half as bright in both cases

As the object moves from just outside the focal point of a converging lens to just inside it, the image goes from _________to ________.

Large and inverted large and upright

Two beams of coherent light travel different paths, arriving at point P. If the maximum destructive interference is to occur at point P, what should be the path difference between the two waves?

The path difference between the two waves should be one-half of a wavelength

In a double-slit experiment, two beams of coherent light traveling different paths arrive on a screen some distance away. What is the path difference between the two waves corresponding to the third bright band out from the central bright band?

Source : quizlet.com

## The Speed of Light and the Index of Refraction

"" ""

Have you heard these statements before? They are often quoted as results of Einstein's theory of relativity. Unfortunately, these statements are somewhat misleading. Let's add a few words to them to clarify. "" ""Those additional three words are very important. A vacuum is a region with no matter in it. So a vacuum would not contain any dust particles (unlike a vacuum cleaner, which is generally full of dust particles). Light traveling through anything other than a perfect vacuum will scatter off off whatever particles exist, as illustrated below.

In vacuum the speed of light is

= 2.99792458 x 108 m/s

This vacuum speed of light, , is what the statements from relativity describe. Whenever light is in a vacuum, its speed has that exact value, no matter who measures it. Even if the vacuum is inside a box in a rocket traveling away from earth, both an astronaut in the rocket and a hypothetical observer on earth will measure the speed of light moving through that box to be exactly . No one will measure a faster speed. Indeed, is the ultimate speed limit of the universe. That's not to say that nothing ever travels faster than light. As light travels through different materials, it scatters off of the molecules in the material and is slowed down. For some materials such as water, light will slow down more than electrons will. Thus an electron in water can travel faster than light . But nothing ever travels faster than . The amount by which light slows in a given material is described by the index of refraction, . The index of refraction of a material is defined by the speed of light in vacuum divided by the speed of light through the material :

= /

The index of refraction of some common materials are given below.

material material

Vacuum 1 Crown Glass 1.52

Air 1.0003 Salt 1.54

Water 1.33 Asphalt 1.635

Ethyl Alcohol 1.36 Heavy Flint Glass 1.65

Fused Quartz 1.4585 Diamond 2.42

Values of come from the

The values of depend somewhat on wavelength, but the dependence is not significant for most applications you will encounter in this course. Unless you are told otherwise, assume the index of refraction given you is appropriate for the wavelength of light you are considering.

Those materials with large indices of refraction are called . (A medium is just a fancy word for a type of material.) Materials with indices of refraction closer to one are called . Being naturally lazy creatures, we generally drop the word "optical'' and talk about dense and rare materials. Just be careful not to confuse dense and rare in the optical context with mass density!

Notice that the index of refraction of air differs from the index of refraction of vacuum by a very small amount. For applications with less than 5 digits of accuracy, the index of refraction of air is the same as that of vacuum, = 1.000.  You will probably not encounter a situation in which the differenc between air and vacuum matters, unless you plan a future in precise optics experimentation.

Even though light slows down in matter, it still travels at an amazing speed, even through a dense material such as lead still travels at an amazing speed.  (Although light does not travel far through lead before being absorbed, high-energy gamma rays can travel a centimeter or so through lead at the speed calculated here.)  Using the definition of , we can find the speed of light through lead:

lead = /lead= (2.99792458 x 108  m/s) /(2.6) = 1.2 x 108 m/s = 2.6 x 108miles per hour

Even slowed by lead, light travels at a speed of 260 miles per hour! That's more than 10,000 times the speed of the orbiting space shuttle. (According to a NASA site, the space shuttle travels 17,322 miles per hour when in orbit.)