A ray of light of frequency is 5.09 x 10^14 Hz is traveling from water to medium X. The angle of incidence in water is 45 degrees and the angle of refraction in Medium X is 29 degrees. Calculate the index of refraction
Snell's law:
sin45*Nwater=Sin29*Nmedium
Nwater= 4/3
Well, well, well, looks like our ray of light is going on a wild adventure! To calculate the index of refraction, we can use Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction. Are you ready for some math?
First, we need to find the sine of the angles. Remember the SOH-CAH-TOA rule? Sine is Opposite over Hypotenuse. So let's get our sines dancing!
For the angle of incidence (let's call it θ1), the sine of 45 degrees is 0.707.
For the angle of refraction (let's call it θ2), the sine of 29 degrees is 0.483.
Next, we can use Snell's law:
sin(θ1) / sin(θ2) = n2 / n1
Since we have the values for sin(θ1) and sin(θ2), we can rearrange the equation to solve for the index of refraction of medium X (n2):
n2 = n1 * (sin(θ2) / sin(θ1))
Now, water has a refractive index of approximately 1.33. So let's do the math:
n2 = 1.33 * (0.483 / 0.707)
And the answer is...
*nervous drumroll*
n2 is approximately 0.911!
So, the index of refraction of medium X is approximately 0.911. I hope this answer brightened your day like a ray of light!
To calculate the index of refraction, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence (θ1) to the sine of the angle of refraction (θ2) is equal to the ratio of the velocities of light in the two different mediums:
n1 * sin(θ1) = n2 * sin(θ2)
where n1 and n2 are the indices of refraction of the first and second mediums, respectively.
Given:
- Frequency of light: 5.09 x 10^14 Hz
- Angle of incidence (θ1): 45 degrees
- Angle of refraction (θ2): 29 degrees
First, we need to convert the angles from degrees to radians:
θ1 = 45 degrees * (π/180) = 0.7854 radians
θ2 = 29 degrees * (π/180) = 0.5061 radians
Now, we can rearrange Snell's Law to solve for the index of refraction for medium X (n2):
n2 = (n1 * sin(θ1)) / sin(θ2)
The index of refraction for water (n1) is approximately 1.33.
Substituting the given values into the equation:
n2 = (1.33 * sin(0.7854)) / sin(0.5061)
Using a calculator, we can evaluate the equation:
n2 ≈ (1.33 * 0.7071) / 0.4848 ≈ 1.927
Therefore, the index of refraction for medium X is approximately 1.927.
To calculate the index of refraction, we can make use of Snell's law, which states:
n1 * sin(angle of incidence) = n2 * sin(angle of refraction)
In this case, the incident medium is water (n1) and the refracted medium is medium X (n2).
Given:
Frequency of light = 5.09 x 10^14 Hz
Angle of incidence (in water) = 45 degrees
Angle of refraction (in medium X) = 29 degrees
Since the frequency of light is not needed for calculating the index of refraction, we can ignore it for now.
First, we need to convert the angles from degrees to radians, as trigonometric functions in most programming languages and calculators usually work with radians.
To convert degrees to radians, we can use the following formula:
radians = degrees * π / 180
Converting the angles to radians:
Angle of incidence (in water) = 45° * π / 180 = 0.7854 radians
Angle of refraction (in medium X) = 29° * π / 180 = 0.5061 radians
Next, we rearrange Snell's law to solve for the index of refraction (n2):
n2 = (n1 * sin(angle of incidence)) / sin(angle of refraction)
Substituting the given values:
n2 = (n1 * sin(0.7854)) / sin(0.5061)
The index of refraction of water (n1) is approximately 1.33.
n2 = (1.33 * sin(0.7854)) / sin(0.5061)
Using a scientific calculator or software, evaluate the sine function for the angles:
n2 = (1.33 * 0.7071) / 0.4848
n2 = 0.9426 / 0.4848
n2 ≈ 1.945
Therefore, the index of refraction of medium X is approximately 1.945.