Concept Check #6 Chapter 25: Visual and Optical Instruments Chapter 26: Relativi

Question

Concept Check #6

Chapter 25: Visual and Optical Instruments
Chapter 26: Relativity

1. A biology student uses a converging lens to examine the details of a small insect. If the focal length of the lens is 12 cm, what is the maximum angular magnification given by the lens? What is the magnification for relaxed-eye viewing?

2. A spacecraft moves past a student with a relative velocity of 0.90c. If the pilot of the spacecraft observes 10 min to elapse on his watch, how much time has elapsed according to the student’s watch?

3. One pair of 25 year old twins takes a round trip through space while the other twin remains on Earth. The traveling twin moves at a speed of 0.95c for a total of 39 years, according to Earth time. Assuming that special relativity applies for the entire trip, what are the twin’s ages when the traveling twin returns to Earth?

4. What speed dilates 2.50 seconds into 50.75 seconds?

5. An astronaut must journey to a distant planet which is 200 light-years away from Earth. What speed will be necessary if the astronaut wishes to age only 10 years during the round trip?

Explanation / Answer

1)Given,

f = 12 cm

We know that maximum angular magnification is given by:

M = 25/f + 1 = 25/12 + 1 = 3.08 = 3.1

Hence, M = 3.1

2)Given,

v = 0.9 c

gamma = sqrt (1 - v^2/c^2)

gamma = sqrt (1 - 0.9c^2/c^2) = 0.44

delta-t = gamma t = 0.44 x 10 = 4.4 min

Hence, t = 4.4 min

[As per guidelines, kindly put one question at a time. I have solved two for you. Kindly check and let me know for any query]

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