Question

Given: The sun is 1.5 × 108 km from Earth. The index of refraction for water is 1.297. 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. a) 3.13551 b) 2.47672 c) 3.07713 d) 2.29326 e) 2.35163 f) 2.20153 g) 3.01042 h) 2.52675 i) 2.25156 j) 2.85198

Answer 1

Answer:

The correct answer is B

Explanation:

For this exercise we must use the definition of the index of refraction

     n = c / v

Where n is the index of refraction, c the speed of light in a vacuum and v the speed of light in the material medium.

    v = c / n

As light travels at constant speed, we can use the equations of uniform motion

    v = d / t

    c / n = d / t

    t = d n / c

Let's calculate the travel time for the vacuum, where the refractive index is  one (n = 1)

     d = 1.5 108 km (1000m / 1 km) = 1.5 10¹¹ m

     t = 1.5 10¹¹ 1/3 10⁸

     t1 = 5 10² s (1min / 60s) = 8.33 min

Now let's calculate the time for water n = 1,297

     t2 = 1.5 10¹¹  1,297 / 3 10⁸

     t2 = 6,485 10² s = 10,808 min

The time difference is the subtraction of these two values

     Δt = t2-t1

     Δt = 10,808 -500

     Δt = 2,478 min

The correct answer is B