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# North Star, frequency of light, radio waves, underwater sun

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The distance to Polaris, the North Star, is approximately 6.44 x 10^18 m. If Polaris were to burn out today, how many years would it take to see it disappear? (b) How long does it take sunlight to reach Earth? (c) How long does it take a microwave signal to travel from Earth to the Moon and back? (The distance from Earth to the Moon is 3.84 x 10^5 km.)

The human eye is most sensitive to light of wavelength 5.50 x 10^-7 m, which is in the green-yellow region of the visible electromagnetic spectrum. What is the frequency of this light?

An important news announcement is transmitted by radio waves to people sitting next to their radios 100 km from the station, and by sound waves to people sitting across the newsroom, 3.00 m from the newscaster. Who receives the news first? Explain. Take the speed of sound in air to be 343 m/s.

Find the speed of light in (a) water, (b) crown glass and (c) diamond

An underwater scuba diver sees the Sun at an apparent angle of 45.0° from the vertical. What is the actual direction of the Sun?

A laser beam is incident at an angle of 30.0° from the vertical onto a solution of corn syrup in water. If the beam is refracted to 19.24° from the vertical, (a) what is the index of refraction of the syrup solution? Suppose the light is red, with vacuum wavelength 632.8 nm. Find its (b) wavelength, (c) frequency, and (d) speed in the solution.

#### Solution Preview

1. The distance to Polaris, the North Star, is approximately 6.44 x 1018 m. If Polaris were to burn out today, a) how many years would it take to see it disappear? (b) How long does it take sunlight to reach Earth? (c) How long does it take a microwave signal to travel from Earth to the Moon and back? (The distance from Earth to the Moon is 3.84 x 105 km.)

Solution:

Speed of light in vacuum is 3 x 108 m/s.

a) Distance of Polaris from earth = 6.44 x 1018 m

Time taken for light to reach earth from Polaris = Distance/Speed = 6.44x1018/3x108 = 2.15x1010 sec .........(1)

1 year = 365 x 24 x 60 x 60 = 3.15x107 sec .........(2)

Hence, dividing (1) by (2) we get : Time taken for light to reach earth from Polaris = 2.15x1010/3.15x107 = 682 years

b) Distance of sun from earth = 1.496x1011 m

Time taken by the sun light to reach earth = 1.496x1011/3x108 = 500 sec = 500/60 = 8.33 min

c) Distance travelled by the microwave = 2 x moon's distance from earth = 2 x 3.84 x 105 = 7.68 x 105 km = 7.68 x 108 m

Time taken by a microwave signal from earth to moon and back = Distance/Speed = 7.68 x 108/3 x 108 = 2.56 sec

2. The ...

#### Solution Summary

North Star, frequency of light, radio waves, underwater sun direction and lasers are examined.

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