Answer :
Answer:
The refractive index of the liquid is 1.3
Explanation:
Refractive index is a dimensionless number that describes how fast light travels through a material.
It is also defined as speed of light in vacuum to speed of light in the medium.
Refractive index = speed of light in vacuum/ speed of light in liquid
Given;
speed of light in vacuum = 4.55 km/t
speed of light in liquid = 3.5 km/t
Refractive index = 4.55/3.5
Refractive index = 1.3
Therefore, the refractive index of the liquid is 1.3
Answer:
Refractive index of the liquid = 1.3
Explanation:
The refractive index (n) also called the index of refraction is the ratio of the velocity/speed of light in free space (air or vacuum) to the velocity/speed of the light as it passes through another medium (say liquid).
The refractive index (n) has no unit and is given by;
n = [tex]\frac{V_{v} }{V_{l} }[/tex] -------------------------- (i)
Where, as stated in the question;
[tex]V_{v}[/tex] is the velocity/speed of the light in vacuum and
[tex]V_{l}[/tex] is the velocity/speed of the light in liquid
[tex]V_{v}[/tex] = distance traveled by light in vacuum / time taken in the vacuum
[tex]V_{l}[/tex] = distance traveled by the light in the liquid / time taken in the liquid.
Since the times taken are the same in both the vacuum and the liquid, let the times taken be t.
=> [tex]V_{v}[/tex] = distance traveled in vacuum / t = 4.55/t
=> [tex]V_{l}[/tex] = distance traveled in liquid / t = 3.50/t
Substituting for the values of [tex]V_{v}[/tex] and [tex]V_{l}[/tex] in equation (i), we have;
=> n = [tex]\frac{4.55/t}{3.50/t}[/tex]
=> n = [tex]\frac{4.55}{t}[/tex] ÷ [tex]\frac{3.50}{t}[/tex]
=> n = [tex]\frac{4.55}{t}[/tex] x [tex]\frac{t}{3.50}[/tex]
=> n = 1.3
The refractive index of the liquid is 1.3