A beam of light passes from air to ethanol, with index of refraction of 1.36. If the angle of incidence ( 1) is 30.0 degrees, then calculate the angle of refraction, after light passes through ethanol and enters into air.
A. 15.3 degrees
B. 21.6 degrees
C. 30.0 degrees
D. 39.8 degrees
I tried it and got C??
The answer can be found using the following method:
Index of refraction 1[wtf is this?: air = 1.00] * Sin(30)[wtf is this?: 30 degrees]
all of that is equal to =
Index of refraction 2[wtf is this?: 1.36 {water is 1.33 just fyi}] * Sin(??) [wtf is this?: what you are asked to find]
Okay now that I've laid that out for your lazy procrastinating undisciplined drudering self:
1.00 * Sin(30) or 1.00 * 0.5, because the Sin(30 degrees) = 0.5
So the 1.00 * 0.5 = 1.36 * some number that is the same as saying Sin(??some angle??)
Let me grab my graphing calculator you slovenly procrastinating not doing what you are supposed to person...
(1.00*0.5)/1.36 = 0.3676470588
BUT WAIT, THERE'S MORE!
That isn't the angle you are looking for.
Remember how I took the sin of 30 degrees and got 0.5? This last number is the same kind of dude. We have to Sin^-1(0.3676470588) to find our angle. [WTF does that mean?: it means inverse Sin (bla number) = an angle]
And just you know, since you don't study like you should, that bla number is actually a fraction between 0 and 1 which represents the height of the triangle in a unit circle. If you don't know wtf that is, you need to catch up and handle yourself, or you're going to be very disappointed in yourself soon...
HANDLE YOUR BUSINESS!
its B
To solve this problem, 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 of the two media.
The formula for Snell's law is:
n1 * sin(1) = n2 * sin(2)
where:
- n1 is the index of refraction of the medium the light is coming from (in this case, air).
- 1 is the angle of incidence.
- n2 is the index of refraction of the medium the light is entering (in this case, ethanol).
- 2 is the angle of refraction.
Let's calculate the angle of refraction using this formula:
n1 * sin(1) = n2 * sin(2)
1.00 * sin(30.0) = 1.36 * sin(2)
Sin(2) = (1.00 * sin(30.0)) / 1.36
Sin(2) = (0.5) / 1.36
Sin(2) = 0.3676
Now, to find the angle of refraction, we need to take the inverse sine (sine inverse) of the value we just calculated.
2 = sin^(-1)(0.3676) ≈ 21.6 degrees
So, the correct answer is B. 21.6 degrees.
To calculate the angle of refraction, you can use Snell's law, which states that the ratio of the sines of the angles of incidence and refraction is equal to the ratio of the indices of refraction of the two mediums:
n1 * sin(1) = n2 * sin(2),
where n1 is the index of refraction of the medium the light is coming from (air in this case), 1 is the angle of incidence, n2 is the index of refraction of the medium the light is entering (ethanol in this case), and 2 is the angle of refraction.
In this example, the index of refraction of air is approximately 1, and the index of refraction of ethanol is 1.36.
Plugging these values into Snell's law, we have:
1 * sin(30.0) = 1.36 * sin(2).
Rearranging the equation to solve for sin(2):
sin(2) = (1 * sin(30.0)) / 1.36
sin(2) = (0.5) / 1.36
sin(2) ≈ 0.3676
To find the angle of refraction, 2, we can take the inverse sine (also known as arcsine) of the value we just calculated:
2 ≈ arcsin(0.3676) ≈ 21.6 degrees.
Therefore, the correct answer is B. 21.6 degrees.