Homework #4

A pair of toy cart wheels is rolled obliquely from a smooth surface onto two plots of grass, a rectangular plot and a triangular plot, as shown below. The ground is on a slight incline so that, after slowing down in the grass, the wheels will speed up again when emerging on the smooth surface on the opposite end. Finish each sketch by showing some positions of the wheels inside the plots on the other sides, thereby indicating the direction of travel.

(In Notebook)

Consider Fermat's Principle of Least Time. Now, consider the incident beam that will be reflected off of the mirrored surface in each of the cases below. Accurately draw the reflected beam in each of the following cases.

(in notebook)

Consider Fermat's Principle of Least Time. Now, consider the reflection of light off of the mirrored surface for each of the cases below, where the light must hit the mirrored surface AND pass through both points A and B. Construct the light beam that will satisfy Fermat's Principle of Least Time for each of the cases.

(in notebook)

Consider the transmission of light through a material, such as white light through glass. Noting that the lowest speed of light ever measured is 28 m/s in nano-Kelvin sodium, find the index of refraction for this nano-Kelvin sodium condensate.

...

If you were to send a beam of laser light to a space station above the atmosphere and just above the horizon, would you aim the laser above, below, or at the visible space station? Explain.

directly at; refraction will curve it down. You are simply reversing the light beam from the station to you

A person in a dark room looking through a window can clearly see a person outside in the daylight, whereas the person outside cannot see the person inside. Explain.

Because it is very bright outside, there is a lot of light reflecting back towards them and because our eyes in reality don't see the people, but the light reflecting off of them from inside. The person in the dark room doesn't reflect enough light compared with the reflection of the glass so the people outside cannot see the people inside.

You can get sunburn on a cloudy day, but you can't get a sunburn even on a sunny day if you are behind glass. Why?

Clouds are transparent to ultraviolet light, which is why clouds offer no protection from sunburn. Glass, however, is opaque to ultraviolet light, and will therefore shield you from sunburn. Glass does not let Ultraviolet light through, but clouds do.

What determines whether a material is transparent or opaque?

If the frequency of the light is the same as the resonant frequency of the electrons, the material is opaque. Transparent materials re-emit light and opaque only absorbs.

What is the advantage of having matte (non-glossy) pages in a book rather than pages with a glossier surface?

If the pages are smooth and glossy the pages would reflect light back and it would be harder to read.

Why would you expect the speed of light to be slightly less in the atmosphere than in a vacuum?

In a vacuum there are fewer atoms to absorb and hamper the movement of the energy.There are interaction delays in the atmosphere. The speed of light would be slightly less in the atmosphere because of interaction delays with atmosphere.The average speed of light will be less where it interacts with absorbing and re- emitting particles of matter, such as in the atmosphere. The greater the number of interactions along the light's path, the less the average speed.

If you fire a bullet through a board, it will slow down inside and emerge at a speed that is less than the speed at which it entered.Does light, then, also emerge from the other end of the glass at a lower speed? Defend your answer.

It doesn't travel at a lower speed when it emerges from the other side of the glass because once it leaves the glass it is traveling through a different medium. It will then travel at the speed through the other medium.

Pretend that a person can only walk at a certain, constant pace. If you time his uninterrupted walk across a room of known length, you can calculate his walking speed. If, however, he stops momentarily along the way to greet others in the room (because there is a party taking place), the extra time spent in his brief interactions gives an average speed across the room that is less than his walking speed. (The average speed is the distance traveled in a given time divided by that time. So, the longer the time for a fixed distance, the slower the speed over that distance.) How is it different from it?

It is different because when the light ray interacts with the atom it gets consumed by an atom and there is then a brand new light ray

When a fish in a pond looks upward at an angle of 45◦, does it see the sky above the water's surface or a reflection from the water-air boundary of the bottom of the pond? Defend your answer.

It sees the sky because 45 is less than the critical angle of water which is 48 which means it can see above the water.

Short wavelengths of visible light interact more frequently with the atoms in glass than do longer wavelengths. A. Does this interaction time tend to speed up or to slow down the average speed of short-wavelength light in glass?

It slows down the average speed because the more it interacts the longer time it takes and thus decreasing the average speed.

Consider Fermat's Principle of Least Time. What is the statement of this principle?

It stated that light will always take the path from one point to another that minimizes the time of its journey.

Consider Fermat's Principle of Least Time. Consider two points in vacuum through which light must travel. What type of path will the light take in traveling through these points?

It will travel in a straight line because there are no delays and the quickest way to get to a place without delays is in a straight line.

Consider the transmission of light through a material, such as white light through glass. Provide a detailed explanation of why the light travels slower in this material than when it travels in a vacuum.

Light travels slower through glass than in a vacuum because in glass there is this delay due to the light interacting with matter, as opposed to vacuum where it does not experience any delays

Consider the following parts which deal with the refraction of light. A. Look at the figure below and notice how the ray is bending in going from Medium 1 into Medium 2. Which medium has the larger index of refraction?

Medium 2 has a larger index of refraction

Consider the following parts which deal with the refraction of light. Look at the figure below and notice how the ray is bending in going from Medium 1 into Medium 2. Which medium has the smaller index of refraction?

Medium 2 has the smaller index of refraction

Consider the following parts which deal with the refraction of light. Look at the figure below, which has a light beam from some fixed medium in some fixed orientation hitting three different media (A, B, and C). Rank the media in order, from the one with the highest index of refraction to the one with the lowest index of refraction.

Medium A, Medium C, Medium B

Is glass transparent to light of frequencies that match its own natural frequencies? Explain.

No, glass is not transparent to those waves, because of resonance: they drive the glass molecules to oscillate at their natural frequencies, building up amplitude and holding onto the energy long enough that collisions can occur whereby the energy is transformed to heat in the glass (i.e. absorbed).

To reduce glare from the surroundings, the windows of some department stores, rather than being vertical, slant inward at the bottom. How does this reduce glare?

So light reflected off the front surface reflects away from your eyes. If the windows were vertical the sun would be able to reflect right through. Due to the windows being slanted, this allows for the sunlight to refract and allow the sunlight to reflect down. Instead of reflecting straight through.

What exactly are you seeing when you observe a "water-on-the-road" mirage, as below?

The light goes close to the ground, but the air is thinner, so it bends and has a refraction so it looks like you can see water on the road.

Car mirrors are uncoated on the front surface and silvered on the back surface. When the mirror is properly adjusted, light from behind reflects from the silvered surface into the driver's eyes. This is a good thing, because you want to be able to see whatever is behind your car. However, this is not so good at nighttime with the glare of headlights from cars behind you. This problem is solved by the wedge shape of the mirror, which is shown below. When the mirror is tilted slightly upward to the "nighttime" position, glare is directed upward toward the ceiling, away from the driver's eyes. Yet the driver can still see the cars behind him using the rearview mirror. Explain why this is the case.

The mirror is wedge shaped; in normal position, the silvered back surface is responsible for the reflection into the driver's eyes. By tilting the wedge angle of the glass up, the silvered surface (reflective) goes up too; a dramatic reduction of brightness (glare) from the car behind. However, the driver can still see cars behind. Two surfaces of the mirror reflect light. The front surface reflects about 4% of the incident light, and the silvered surface reflects most of the rest. When the mirror is tilted in the "daytime" position, the driver sees light reflecting from the silvered surface. In the "nighttime" position, with the mirror tilted upward, light reflecting from the silvered surface is directed above the driver's view and the driver sees light reflected from the front surface of the mirror. That 4% of rearview light is adequate for night driving. Because you tilt it at a different angle it has a different angle of reflection.

Consider driving at night under various conditions. A. Which kind of road surface is easier to see when driving at night: a pebbled, uneven surface or a mirror-smooth surface?

The pebbled uneven surface because it reflects more light back to the eye. The pebbly uneven surface is easier to see. Light reflected back from your headlights is what lets you see the road. The mirror-smooth surface might reflect more light, but it would reflect it forward, not backward, so it wouldn't help you see.

Consider the image below. How would the reflected light appear if the water surface was perfectly smooth?

The sun would look round because the surface is perfectly smooth it would it would mirror a perfect image this is because there's specular reflection.

A pulse of red light and a pulse of blue light enter a glass block at the same time normal to its surface. Strictly speaking, after passing through the block, which pulse exits first?

The red light exits first. The red pulse will exit the glass block before the blue pulse. Dispersion is the relationship between frequency of light and the refractive index. Refractive index represents how much light slows down inside of a medium. Since the blue pulse has a higher index in glass, it will travel more slowly and emerge after the red.

Does a diamond under water sparkle more or less than in air? Defend your answer.

The sparkling of a diamond actually occurs because of repeated "total internal reflection". When light enters a diamond, it is difficult for it to leave because of the high index of refraction. All the bouncing means that light leaves the diamond in many different directions, leading to the sparkle. Putting a diamond underwater means that the difference in speeds (or index of refraction) is much less which leads to less total internal reflection, and therefore, less sparkling!

Suppose that sunlight falls both on a pair of reading glasses and on a pair of dark sunglasses. Which pair of glasses would you expect to become warmer more quickly? Defend your answer.

The sunglasses will be warmer in sunlight than regular reading glasses because the reading glasses transmit most of the light energy that is incident upon them, whereas the sunglasses absorb more light energy, thus increasing their internal energy.

We know that the speed of light within glass is slower than in air. However, recall that the speed of light obeys the following equation c = fλ, where c is the speed of light, f is the frequency of the light, and λ is the wavelength of the light. So, if the speed of light changes in going from one medium to another, does any of the other mentioned quantities change? Explain.

The wavelength changes as well, where the index of refraction can also be stated in terms of wavelength where the index of refraction is equal to wavelength in vacuum over wavelength in medium.

Describe, in detail—with appropriately drawn ray-trace diagrams—the refraction effects seen in the pictures below. Why does the pencil appear "bent" at the water-air interface?

This happens because at the boundary between air and water the light ray refracts. Light rays from the submerged part of the pencil will intersect in a different location than the light rays from the portion of the pencil that extends above the water.

18-wheelers (also known as big-rigs) have signs on their back ends that say, "If you can't see my mirrors, I can't see you." Explain the physics behind this expression.

This is because in order for someone to see the reflected beam there has to be an incident beam that shows the person behind them. In any mirror if you can see a person they will also be able to see you. This is because the incidence angle and the reflected angle are exactly the same. Light that takes a path from one point to another will take the same path when it goes in reverse direction.

Consider the transmission of light through a material, such as white light through glass.Consider the following table of indices of refraction for various optically transparent materials.With this table in mind, explain why the equation for the speed of light in a material, denoted as v, has the form v=c/n where c = 3.0 × 10^8 m/s is the speed of light in vacuum, and n is the index of refraction of the material under consideration.

This is because it is understood that there are delays caused by light interacting with matter where v < c and meaning n > 1 and n takes into account the delays that there are in different materials.

Describe, in detail—with appropriately drawn ray-trace diagrams—the refraction effects seen in the pictures below. Why does one see a "reflection" of the tree-lined landscape in the ground?

This is because of the changeable speed of light and because the air is warmer and less dense near the ground and the wave fronts pick up speed (because there's less interaction with atoms) and as they travel downward, making them bend upward. So, when the observer looks downward, he sees the top of the tree.

Provide an explanation for the following picture, which shows a lady seemingly floating.

This is because she has a mirror between her legs which gives an illusion that she of floating, when in reality she is standing on one leg and the mirror is just reflecting her right leg.

In the picture below, why is the red laser beam reflecting at the interface between the lucite and the air rather than transmitting into the air from within the Plexiglas?

This is because total internal reflection is occurring which is the complete reflection of light back into its original material and for every incident beam there is there will also be a reflected and a transmitted beam.

Why does the coin inside the container below look so magnified and close to the surface as compared to the coin outside the container (which is an identical height below the position at which the picture was taken)?

This is because water has a different density than air which causes the light to change direction inside of it. This causes refraction. Water is also curved which makes which bends light as it comes out from the water and it to look magnified.

Consider the transmission of light through a material, such as white light through glass.Looking at the table again, comment on why the table includes the frequency/wavelength of light used in the measurements of these indices of refraction.

This is because when light travels from one medium to another the speed changes and so does the wavelength. The frequency is also included because of the different frequencies different colors of light bend at in which red light bends the least (lowest frequency) and blue light bends the most(highest frequency).

Consider driving at night under various conditions. Why is it difficult to see the roadway in front of you when driving on a rainy night?

This is because when the road is wet it there is less diffuse reflection and it is harder to see.

Consider Fermat's Principle of Least Time. Now, consider the fact that for this principle of Fermat, that it is of least time rather than of least distance. Now, recall our analogy of a lifeguard trying to save a drowning surfer in the ocean.The way in which the lifeguard travels to minimize the time it takes for him to reach the drowning person is identical to how the light travels when going from one transparent medium (say air) to another (say water). This is illustrated in the diagram below, where the lifeguard is able to minimize the time he takes to reach the drowning person by traveling along the (circled) path B. Notice that path A is the shortest distance out of all the shown possibilities. So, why does shortest distance not imply shortest time in this case?

This is because your average speed in water is significantly slower than your average speed on concrete. Therefore, it will take a significant more amount of time to travel through path A because although it may be the shortest distance a good amount of that distance traveled will be traveled at a significantly slower speed than if taking path B.

Consider the image below. A. Why does the reflected light from the Sun appear as a column in the body of water shown above?

This is due to the fact that there is a diffuse reflection and because of the bumpy surface it illuminated different as if the waves were still.

Pretend that a person can only walk at a certain, constant pace. If you time his uninterrupted walk across a room of known length, you can calculate his walking speed. If, however, he stops momentarily along the way to greet others in the room (because there is a party taking place), the extra time spent in his brief interactions gives an average speed across the room that is less than his walking speed. (The average speed is the distance traveled in a given time divided by that time. So, the longer the time for a fixed distance, the slower the speed over that distance.) A.How is this similar to light passing through glass?

This is similar because the constant speed can represent the speed of light in vacuum and the delayed time can represent the speed in a medium that is not air due to the delays that are experienced due to the interactions with the atoms. That will then give you the speed of light in that medium.

Consider the transmission of light through a material, such as white light through glass. Specifically considering glass, provide a detailed explanation for why UV radiation doesn't transmit through glass.

Ultraviolet radiation resonates with the atoms. Glass atoms hold on to UV energy, the transmitted energy takes the form of heat instead of light. So glass is not transparent to ultraviolet radiation.

Suppose you are viewing the man looking at himself from the perspective shown below. What is wrong with the image of the man according to you? (Try it with a friend or family member to further investigate the issue!)

We would not see an image of the man in the mirror as shown. If he is viewing himself, then we wouldn't also be able to see his image unless we were in back (or in front) of him. If we are to stand to the side of the man and see him and an image of him in the mirror, then the mirror cannot be exactly in front of him. The mirror would have to be located to the man's right, as shown in the sketch. The man's view would miss the mirror completely.

Cowboy Joe wishes to shoot his enemy by ricocheting a bullet off of a mirrored plate. To do so, should he simply aim at the mirrored image of his enemy? Explain.

Yes, Cowboy Joe should simply aim at the mirrored image of his assailant. The bullet ricochets off the metal plate in such as way that its angle of incidence equals its angle of rebound. This is the same rule that the light follows when reflecting, so the bullet will just retrace the light ray's path, in the reverse direction.

Short wavelengths of visible light interact more frequently with the atoms in glass than do longer wavelengths. Then, does the index of refraction depend on the frequency of light? Explain.

Yes, as can be seen where red light has the lowest frequency and blue light has the highest frequency, in which red light bends the least and blue light bends the most showing that it is going from a fast to a slow medium.

If you fire a bullet through a board, it will slow down inside and emerge at a speed that is less than the speed at which it entered. Does light, then, similarly slow down when it passes through glass? Explain.

Yes, this is only true if it had previously been traveling through air because the fastest medium light will travel at is through air and anything other than that it will travel slower.

Your eye looks into the mirror from the position indicated in the diagram below. Which of the numbered cards can you see reflected in the mirror? Why?

You can see it in card number 2, this is because the angle of incidence and the angle of reflection are the same, meaning that that is where the beam of reflection would hit.

Suppose you're standing on a bank when you notice that there is a fish in the water. Now, suppose that the fish was small and blue, and that your laser light was red. What correction should you make in zapping the fish with your laser light? Explain.

You should aim above because blue light bends the most and red light bends the least

Suppose you're standing on a bank when you notice that there is a fish in the water. You wish to spear the fish beneath the water surface in front of you. Should you aim above, below or directly at the observed fish to make a direct hit? Defend your answer.

You should aim below because your eyes are not seeing the actual location of the fish because the light coming from the fish is refracting as it passes into the air and to your eye, so you will see the fish closer to the surface than what it actually is.

Suppose you're standing on a bank when you notice that there is a fish in the water. If, instead, you want to zap the fish with a laser, should you aim above, below, or directly at the observed fish? Defend your answer.

You should aim directly at the fish because the light will refract as it enters the water following the exact reverse path as the light coming from the fish to your eye. This way it allows you to ignore refraction and hit the fish by just aiming at it.