GEOG 1216 Chapter Notes -Natural Hazard, Natural Disaster, No Trend

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1badleroybrown

20 Jul 2022

School

University of Denver

Department

Geography

Course

GEOG 1216

Professor

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Document Summary

Worksheet: trends in the incidence and distribution of hazards. During class today, you will have the opportunity to explore graphs and charts that explore trends in the incidence and distribution of hazards. The data are available in a powerpoint posted on canvas. The most up-to- date data come from: https://ourworldindata. org/natural-disasters; this is a great source of hazards data. Goals of the exercise: to practice interpreting data from graphs, charts, and maps, to develop skills in identifying trends from complex data, to provide thematic information on trends in the incidence and distribution of hazards, explore the dataset. First, go to ourworldindata. org and explore the information in the about tab. Then, spend a few minutes familiarizing yourself with what is in the powerpoint before completing the questions listed in part b. As you work through the questions in part b, consider the trends that you see in the following areas.

Related Questions

a) For an image that is in front of a mirror, is the imagedistancepositive or negative?
b) Given the image distance, what additional information isneededto determine the focal length? Explain.
c) For an inverted image is the image height positiveornegative?
d) Given the object and image heights and a statement as towhetherthe image is upright or inverted, what additionalinformation isneeded to determine the object distance?
e) A small statue has a height of 3.5 cm and is placed in front ofaconcave mirror. The image of the statue is inverted, 1.5 cmtall,and is located 13 cm in front of the mirror. Find the focallengthof the mirror.

a) The drawing shows a ray of light traveling throughthreematerials whose surfaces are parallel to each other. Therefractedrays (but not the reflected rays) are shown as the lightpassesthrough each material. Taking into account the relative sizesofthe angles of incidence and refraction, rank thematerialsaccording to their indices of refraction, greatest first.Providereasons for your rankings.
b) A ray of light strikes the a-b interface ata50.0^o angle of incidence. The index of refractionofmaterial a is n_a = 1.20. The anglesofrefraction in materials b and care,respectively, 45.0^o and 56.7^o. Findtheindices of refraction in these two media

Every transparent material can be characterized by what is called its index of refraction, n, given by the equation

$Chapter 9, Problem 4C, Every transparent material can be characterized by what is called its index of refraction, n, given , example 1$

Here c is the speed of light in a vacuum and v is the speed of light in the transparent material. Although normal air is not quite a vacuum, its density is small enough that v_a_i_ris approximately equal to c, so that we may take $Chapter 9, Problem 4C, Every transparent material can be characterized by what is called its index of refraction, n, given , example 2$ without too much error.
The precise mathematical relationship between the angles of incidence and refraction is given by what is known as Snell’s law,

$Chapter 9, Problem 4C, Every transparent material can be characterized by what is called its index of refraction, n, given , example 3$
where n₁and A₁are the index of refraction and the angle between the light ray and the normal, respectively, in medium 1, and n₂and A₂are the corresponding quantities for medium 2.

(a) Using the information in Table 9.1, compute the index of refraction for water and for fused silica (glass).
(b) Verify the result in Example 9.2 using Snell’s law explicitly. Show, using the same relationship, that the values for the angles of refraction in air (medium 2) in panels (b), (c), (d), and (e) of Figure 9.36 are correct for the given angles of incidence in glass (medium 1).

whitebuffalo354

Relevant information:

For a normal distribution function, F = Aexp(-Î²E), Î² =1/(kT), E =1/2mv^2, A is normalization factor, T is temperature, kis theboltzmann's constant, v is velocity, and m is the mass.

For a fermi distribution function, F =1/(B₁exp(-Î²E)+1).<- This is what I need tosolve

For a boson distribution function, F =1/(B₂exp(-Î²E)-1).<- This is what I need tosolve

For a normal distribution, the relationship between themostprobable velocity and temperature, v = (2kT/m)^(1/2), To getthisequation, the book used 3D space. F d³v=Aexp(-1/2Î²mv_x²-1/2Î²mv_y²-1/2Î²mv_z²)d³v.A new function for one axis is defined G dv=A'exp(-1/2Î²m_x²) and to normalizethisfunction, the integral from -infinity to +infinity of functionG isdefined as 1. So, A'(2Ï/(Î²m))^(1/2) = 1 and A'is(Î²m/(2Ï))^(1/2). Since function F is in 3D space, A=(Î²m/(2Ï))^(3/2). The book defined the volume of aspherical shellwith velocity v to be 4Ïv²dv, so Fdv =4ÏAexp(-1/2Î²mv²)v² dv. To findthe mostprobable speed of the distribution function, thederivative is takenand it is set to 0. So it looks likethis:exp(-1/2Î²mv²)(2v)-1/2Î²m(2v)exp(-1/2Î²mv²)v²=0. The book skipped a lot of steps but the tricky matheventuallyreduced to v = (2kT/m)^(1/2). <- This is the typeofrelationship I am looking for

Problem:

I do not know how the book did this math but I have to dosomethingsimilar with the Fermion and boson functions to get thevelocity totemperature relationships for each of thefunctions.

GEOG 1216 Chapter Notes -Natural Hazard, Natural Disaster, No Trend

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