PHL205H1 Lecture Notes - Good And Evil, Omnipotence, Manichaeism

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lemonrhinoceros500

14 Oct 2012

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The second question is especially pressing for someone who holds that the world is the creation of a good god. Let s address these questions one by one: what is evil, augustine"s early (manichean) view of evil: They imagine it to be a malignant mind creeping through the earth. And since piety forbade me to believe that the good god had created an evil nature, I concluded that there are two opposed masses, both infinite, but the evil rather smaller, the good larger. (conf. 5. 10. 20; see also 7. 5. 7: evil has existed, but god did not create the evil, therefore there must be an opposed nature. Then there must be two fundamental cosmological principles: god and the principle of evil. 7. 2. 3): the idea of two opposite principle is impossible. If you say they have to interact this can mean two things: they have to because (a) of something intrinsic to them or (b) because of something extrinsic.

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Astronomers have observed a small, massive object at the centerof our Milky Way galaxy. A ring of material orbits this massiveobject; the ring has a diameter of about 15 light years and anorbital speed of about 200 km/s.
A) Determine the mass of the massive object at the center of theMilky Way galaxy.
Take the distance of one light year to be 9.461Ã10¹⁵m. Iwas able to get this it is 4.26Ã10³⁷kg.
B) Express your answer in solar masses instead of kilograms, whereone solar mass is equal to the mass of the sun, which is1.99Ã10³⁰. I got this to it is 2.14Ã10⁷ solarmasses
C)Observations of stars, as well as theories of the structure ofstars, suggest that it is impossible for a single star to have amass of more than about 50 solar masses. Can this massive object bea single, ordinary star? I got this it is no.
D) Many astronomers believe that the massive object at the centerof the Milky Way galaxy is a black hole. If so, what is itsSchwarzschild radius? Express your answer in meters.
E)Would a black hole of this size fit inside the earth's orbitaround the sun? The mean distance from the sun to the earth is1.5Ã10^11m.
Please solve part D and E. For part D please show equations andsolve all the way through. I worked it twice and I am getting myanswer wrong. I am afraid I am making a silly mistake.

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.

greenduck607

You will be utiizing a basicoptic system.

The index of refraction of theplastic cylindrical lens depends on wavelength. Choose an anglewhich gives a good color separation and measure the index ofrefraction for blue and red light.

Question:How big is the difference in indices of refraction? How good is theapproximation that n is constant for thismaterial?

If this question doesnt make sense..then just answer ittheoretically speaking. That is how would we go about checkingwhether or not it conforms with the n as the constant for thematerial... Thanks!

Background info:

ThePhysics

The Law ofReflection

The law of reflection states that for a plane mirror, the angle ofincidence is equal to the angle of reflection, and that the tworays lie in a plane.

normal

. A light ray perpendicular to the surface has an angle ofincidence 0Â°.

The Law of Refraction âSnellâs Law

A ray of light passing from one substance (index ofrefraction

n_{1)into another (index of refraction n}

2) across a plane boundary will be refracted. The angle the raymakes in one medium will be related to the angle in the secondmedium by the equation below, and that all rays lie in aplane.

(2)

Total InternalReflection

A ray incident on a medium with lower index of refraction willbe

totally internally reflected if sin Î¸1> n2/n1.There will be no transmitted beam for this incident angle. Ameasurement of the critical angle for total internalreflection can be used to determine the index of refraction of the substance.If n

2 = 1 (air), then the critical angle is:

sin Î¸c = 1/

1. (3)

Polarization byReflection â Brewsterâs Angle

If the angle between the reflected and refracted rays is 90Â°,then

tan Î¸

B = n2/n

1. (4)

At this angle, only light with polarization out of the plane ofreflection and refraction will be reflected. The reflected lightwill be completely polarized.

Figure3.

Refractionof Light Rays

Figure2.

Incidentand Reflected Rays

(1)

Always measure the angles with respect to the surface

PHL205H1 Lecture Notes - Good And Evil, Omnipotence, Manichaeism

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