Given:The sun is 1.5×108km from Earth.
The index of refraction for water is 1.346. How much longer would it take light from the sun to reach Earth if the space between them were filled with water rather than a vacuum?
Answer in units of min.
The sun is 1.5×108km from Earth. The index of refraction for water is 1.346. How much longer would it take light from the sun to reach Earth if the space between them were filled with water rather than a vacuum?
Share
The distance of the Earth from the Sun is:
d = 1.5 × 108 km = 1.5 × 1011 m
The refractive index of water is:
μ = 1.346
The refractive index (μ) is defined as:
μ = speed of light in vacuum / speed of light in the material = c / v
Thus, the speed of light in water is:
v = c / μ
Given:
c = 3 × 108 m/s
Calculate the speed of light in water:
v = 3 × 108 m/s / 1.346 = 2.229 × 108 m/s
The time taken by light to reach the Earth when traveling through water is:
time = d / v = 1.5 × 1011 m / 2.229 × 108 m/s = 0.673 × 103 s
Convert the time to minutes:
t = 673 s
t = 673 / 60 min = 11.22 min
Final Answer:
The time taken for light to reach the Earth when the medium is water is:
t = 11.22 min