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? 1. 3.13551 2. 2.47672 3. 3.07713 4. 2.29326 5. 2.35163 6. 2.20153 7. 3.01042 8. 2.52675 9. 2.25156 10. 2.85198 Answer in units of min.

Answer 1

Answer:

option (2) 2.47672

Explanation:

Data provided in the question:

Distance between the sun and the Earth = 1.5 × 10⁸ km = 1.5 × 10¹¹ m

The index of refraction for water = 1.2973

Now,

Speed of light in water, v = $\frac{\textup{Speed of light in vacuum}}{\textup{Refractive index of water}}$

also,

speed of light in vacuum = 3 × 10⁸ m/s

thus,

Speed of light in water, v = $\frac{3\times10^8}{\textup{1.297}}$  m/s

now,

if the space between the sun and the Earth is filled with water, time (t) taken by the light to reach Earth from sun will be

Time = $\frac{\textup{Distance between the Sun and the Earth}}{\textup{Speed of light in Water}}$

or

Time = $\frac{1.5\times10^{11}}{\frac{3\times10^8}{\textup{1.297}}}$

or

Time = 648.5 seconds

Time taken by light to reach Earth in vacuum

= $\frac{\textup{Distance between the Sun and the Earth}}{\textup{Speed of light in Vacuum}}$

or

Time = $\frac{1.5\times10^{11}}{3\times10^8}$

or

Time = 500 seconds

Therefore,

the difference in time = 648.5 - 500 = 148.5 seconds

or

= $\frac{\textup{148.5}}{\textup{60}}$  minutes

= 2.475 minutes ≈ 2.47672

Hence, the correct answer is option (2) 2.47672

Answer 2

The light will take 149.35 seconds or 2.48 minutes more to reach the earth if the space is filled with water.

Option B shows the correct time difference.

What is the speed?

The speed of an object is defined as the total distance traveled by the object per unit time interval.

Given that the distance d between the sun and the earth is  1.5 × 10^8 km. The refractive index of water is 1.297.

We know that the speed of light in a vacuum is 3 x 10^8 m/s. The speed of light in water is calculated as given below.

$v'= \dfrac {v}{\mu}$

where v is the speed of light in vacuum, v' is the speed of light in water, and $\mu$ is the refractive index of water.

$v' = \dfrac {3\times 10^8}{1.297}$

$v' = 2.31 \times 10^8 \;\rm m/s$

If the region between the sun and earth is filled with water then, the time taken by the light to travel is calculated as given below.

$t' = \dfrac {d}{v'}$

$t' = \dfrac { 1.5 \times 10^8\times 10^3}{2.31 \times 10^8}$

$t' = 649.35 \;\rm s$

If the region between the sun and earth is filled with a vacuum then, the time taken by the light to travel is calculated as given below.

$t = \dfrac {d}{v}$

$t = \dfrac {1.5 \times 10^8 \times 10^3}{3\times 10^8}$

$t = 500 \;\rm s$

The difference in time taken by the light is given as below.

$T = t' - t$

$T = 649.35 - 500$

$T = 149.35 \;\rm s$

$T =\dfrac{ 149.35 }{60}\;\rm min$

$T = 2.475 \;\rm min$

Hence we can conclude that the light will take 149.35 seconds or 2.48 minutes more to reach the earth if the space is filled with water. Option B shows the correct time difference.

To know more about the speed, follow the link given below.

https://brainly.com/question/12759408.