Calculate the index of refraction of a diamond if the speed of light in a diamond is 1.24x10 to the power of 8 m/s.
Please break it down and show all the steps. :) thank you
speed of light in vacuum = 3*10^8 m/s approximately
n = speed of light in vacuum/speed in diamond
n = 3/1.24
= 2.42 approximately
Oh, don't worry, I'm here to make things fun! Now, let's calculate the index of refraction, shall we?
The formula to calculate the index of refraction is:
n = c/v
Where:
n is the index of refraction,
c is the speed of light in a vacuum, and
v is the speed of light in the medium (diamond in this case).
So, all we need to do is divide the speed of light in a vacuum by the speed of light in the diamond.
c = 3.00 x 10^8 m/s (speed of light in a vacuum)
v = 1.24 x 10^8 m/s (speed of light in diamond)
Now, let's do the math:
n = c / v
n = (3.00 x 10^8 m/s) / (1.24 x 10^8 m/s)
And when you plug in those numbers and simplify, you get:
n ≈ 2.42
So, the index of refraction of diamond is approximately 2.42. Easy peasy, right?
To calculate the index of refraction of a diamond, we need to use the formula:
index of refraction (n) = speed of light in a vacuum (c) / speed of light in the medium
Step 1: Given information
Speed of light in a diamond = 1.24 x 10^8 m/s
Step 2: Find the speed of light in a vacuum
The speed of light in a vacuum is a constant value, which is approximately 3 x 10^8 m/s.
Step 3: Substitute the given values into the formula
n = c / vDiamond
= (3 x 10^8 m/s) / (1.24 x 10^8 m/s)
Step 4: Simplify the expression
To simplify the expression, we can divide each term individually:
n = (3 / 1.24) x (10^8 / 10^8) m/s
= 2.419 x 1
= 2.419
Step 5: Determine the final answer
The index of refraction of a diamond is approximately 2.419.
To calculate the index of refraction of a diamond, we need to use the formula:
Index of Refraction (n) = Speed of Light in a Vacuum / Speed of Light in the Material
The speed of light in a vacuum is a well-known constant, which is approximately 3.0 x 10^8 meters per second.
In this case, we are given the speed of light in the diamond, which is 1.24 x 10^8 m/s.
Now, we can substitute these values into the formula:
n = (3.0 x 10^8 m/s) / (1.24 x 10^8 m/s)
First, let's simplify the numerator and denominator:
n = (3.0 / 1.24) x (10^8/10^8) m/s
n = 2.42 x (1/1) m/s
n = 2.42
Therefore, the index of refraction of the diamond is approximately 2.42.
To recap, we used the formula n = Speed of Light in a Vacuum / Speed of Light in the Material, substituted the given values, simplified the fraction, and obtained the final result.