PHYS1002 Study Guide - Final Guide: Virtual Image, Sodium Hydride, Real Image

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olivecaribou938

10 Aug 2018

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PHYS1002

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Chapter 26 the refraction of light: lenses and optical instruments. Light travels through a vacuum at a constant speed, but it travels through materials at a slo(cid:449)e(cid:396) speed. A(cid:272)tuall(cid:455), that(cid:859)s (cid:374)ot (cid:395)uite t(cid:396)ue the speed of the photon is always , but in (cid:373)ate(cid:396)ials, the photo(cid:374) (cid:449)ill i(cid:374)te(cid:396)a(cid:272)t (cid:449)ith the ato(cid:373)s i(cid:374)side it. It(cid:859)s the(cid:374) p(cid:396)one to absorption and re-emission (causing a delay), scattering (changing its path), interference with the fields inside it, and so on. This change in speed can actually cause a change in direction as a light ray deviates from its incident direction to a new medium. To describe this refraction, we use a refractive. Let(cid:859)s defi(cid:374)e the (cid:396)ef(cid:396)a(cid:272)ti(cid:448)e i(cid:374)de(cid:454: because the speed of light in the material is always smaller than the speed of light in a vacuum, this index is always greater than 1 (except for a vacuum).

Related Questions

Electromagnetic radiation is emitted when a charged particle movesthrough a medium faster than the local speed of light. Thisradiation is known as Cerenkov radiation. Cerenkov radiation isfound in many interesting places such as particle detectors andnuclear reactors and can even be seen by astronauts when cosmicrays traverse their eyes. It should be stressed that the particleis never going faster than the speed of light in vacuum (or c),just faster than the speed of light in the material (which isalways less than c). The creation of Cerenkov radiation occurs inmuch the same way that a sonic boom is created when a plane ismoving faster than the speed of sound in the air. The variouswavefronts that propagate in the material add coherently to createan effective shock wave. In this problem, you will become familiarwith this type of radiation and learn how to use its properties toget information about the particles that created it.
A)What is the threshold velocity v_threshold (water) (i.e., theminimum velocity) for creating Cerenkov light from a chargedparticle as it travels through water (which has an index ofrefraction of n=1.33)?
v_threshold (water) =c
B)What is the threshold velocity v_threshold (ethanol) for creatingCerenkov light from a charged particle as it travels throughethanol (which has an index of refraction of n=1.36)?
v_threshold (ethanol) =c
C)Which of the following best explains why neutrally chargedparticles can't give off Cerenkov radiation?

a)Neutral particles are too heavy to emit radiation.
b)Neutral particles don't interact with the electromagnetic fieldsof the medium.
c)Neutral particles can't move above the threshold velocity forCerenkov radiation.
d)Charged particles hit the nuclei of the material more often andthus create more radiation

Huygens' principle (first described by the Dutch scientist Christiaan Huygens in 1678) uses geometry to determine the shape of a wavefront at a time t, given some initial wavefront at an earlier time. This can be constructed by imagining that the initial wavefront is a source of wavelets that propagate from each point at the speed of light. From this principle, one can determine the angles of reflection and refraction by considering the speed of light at each point on the wavefront. In this problem, we will explore some of these concepts.

Part A

First, let's look at a plane wave that is incident on a flat piece of material with an index of refraction n. Part of the light is transmitted through the material and part of it is reflected. For the moment, let's just look at the part that is transmitted. At time t=0, the wavefront is a distance d away from the surface of the material. At time t=t₁, the wavefront is at the position of the material interface. Use the Huygens' principle to determine how far into the material (d') the wavefront has propagated by time t=2t₁.

Express your answer in terms of the variables n, t₁, and the speed of light in a vacuum c.

Note that there would be no change in the direction of the wavefront at any point because the wavefront encountered the material interface at the same time at all points. Thus, all of the individual wavefronts all propagated at the same speed, thereby maintaining the flat wavefront.

Now, instead of having a flat wavefront propagating normal to the material interface, we have a flat wavefront propagating toward the material at an angle of 55° to the axis perpendicular to the material interface. In this part, we will look at the relative positions of a few points—A, B, and C—on the wavefront to illustrate Huygens' principle. (Intro 1 figure) Point C touches the vacuum/material interface at time t=0 whereas point B is a distance d and point A is a distance 2d away from the interface.

Part B

What is the time t_B it will take for point B of the wavefront to encounter the vacuum/material interface?

Express your answer numerically to two decimal places in units of t₁ (the time it takes light to travel a distance d in a vacuum).

It should be noted that the accuracy of the method increases the smaller the distance is before making a new wavefront and redoing the wavelets. If you tried to just draw a large wavelet from point B, then it would hit the surface after only traveling a distance d. This large wavelet would make it difficult to visualize how to add up all of the other wavelets to make a coherent wavefront. As a result, one should just draw a line perpendicular to the wavefront at point B until it hits the surface, at which point the wavelets will change owing to the new index of refraction.

Part C

How far did point C go into the material interface in the time t=t_B that it took for point B to get to the interface? For this part we are looking for the distance traversed by the point C in the material (d_C).

Give your answer in terms of the time t_B, c, and n.

Part D

What is the new angle θ at which point C of the wavefront is propagating (relative to a line perpendicular to the vacuum/material interface)? Try to use the fact that you have a spherical wavefront propagating from t=0 at the point where C met the vacuum/material interface until time t_B when the wavefront at point B reached the interface.

Express your answer in terms of inverse trigonometric functions and n.

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PHYS1002 Study Guide - Final Guide: Virtual Image, Sodium Hydride, Real Image

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