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Define the relative refractive index difference for an optical fiber and show how it

May be related to the numerical aperture. A step index fiber with a large core diameter compared with the wavelength of the transmitted light has an acceptance angle in air of 22° and a relative refractive index difference of 3%. Estimate the numerical aperture and the critical angle at the core–cladding interface for the fiber.



3. Measurements show that 500 muon fall on the top of Mt. Washington altitude 2000m. Muons travel at 99% the speed of light or 0.99 x 3.0 x 108 m/s.

a. Calculate the time in microseconds it would take muon to travel from the top of mt. Washington to its base.

b. Use your calculation and the muon clock graph to find how many muons should reach the bottom of Mt. Washington.

4. Experiments show that the actual number of muons that reach the base of Mt. Washington is 400.

a. According to your muon clock graph, how much time has elapsed if 400 muons reach the base of Mt. Washington?

b. By what factor do the times you found differ?

c. Suggest an explanation for this difference.



2. The half-life of muons provides you with a muon clock. Plot a graph of the number of muons versus time. Use 500 muons as the size of the sample. This graph will become your clock.

a. If 125 muons remain, how much time has elapsed?

b. If 31 muons remain, how much time has elapsed?

c. If 300 muons remain, how much time has elapsed?

d. If 400 muons remain, how much time has elapsed?



Investment

A person may earn ₱100,000.00 by investing in the stocks of an international 

company with a probability of 0.40 or lose ₱35,000.00 over the same period 

with a probability of 0.60. Let X denote the net gain of a person who will invest 

in the company, construct the probability distribution of X, and compute for 

the expected value of a person who will invest in the same company. Interpret 

the result


From the given Demand schedule for air tickets, calculate elasticity of demand



Price of Air Quality Ticket (Per ticket) (Tickets per month)


100000 5000


120000 3500

Calculate the energy stored in elastic material with K=1500NM and applied force at 750N

Elaborate the term elasticity of supply and explain any three factors that determines elasticity of supply

6. A throttling calorimeter is connected to the superheated steam line supplying steam to the auxiliary feed pump on a ship. The line pressure measures 2.5 Mpa. The calorimeter pressure is 110 kpa and 150oC. Determine the entropy of the steam line. Please explain the answer.


Answer: a. 6.8 KJ/kg-oK c. 6.6 KJ/kg-oK

b. 6.2 KJ/kg-oK d. 7.5KJ/kg-oK


We know that 10% people who purchase cars buy manual transmissions and 90% people purchase automatics.Three people purchase a car. find the probability distribution for the number who purchase automatics

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