Calculate the index (n water) of refraction of water given the angle of incidence and the angle of refraction.
I know that the accepted value for n is 1.33 but I am not sure how to calculate the index. Would I use Snell's law: na sin Qa = nb sin Qb?
Thank you!
yes. I'm sure this question has come from the text section dealing with Snell's Law.
So I just want to make sure I did the math corretly: My value for angle of incidence was 20 degrees and for refraction it was 15 so I did
Sin(20) / sin (15) = 1.32 which is very close to the accepted value.
Is this corret?
Yes, you are correct. Snell's law can be used to calculate the index of refraction (n) of water. The law states:
na * sin(Qa) = nb * sin(Qb)
Here, na is the index of refraction of the initial medium (usually air, which has an index of refraction of approximately 1), Qa is the angle of incidence, nb is the index of refraction of the second medium (in this case, water), and Qb is the angle of refraction.
To calculate the index of refraction of water, given the angles of incidence and refraction, you can rearrange Snell's law and solve for nb:
nb = (na * sin(Qa)) / sin(Qb)
In this case, since the index of refraction of air (na) is approximately 1, you can simplify the equation to:
nb = sin(Qa) / sin(Qb)
Substituting the values of the angles of incidence (Qa) and refraction (Qb) into the equation will give you the index of refraction (n) of water.
Yes, you are correct! To calculate the index of refraction (n) of water using Snell's law, you would need to know the angles of incidence (Qa) and refraction (Qb). The equation you provided, na sin Qa = nb sin Qb, is the correct form of Snell's law.
In this case, na represents the medium of the incident ray (e.g., air) and nb represents the medium of the refracted ray (e.g., water). Since you are calculating the index of refraction of water, you would use na = 1 (since air has an index of refraction close to 1) and nb = nwater, where nwater is the index of refraction of water.
To calculate nwater, rearrange Snell's law equation:
nwater = (na sin Qa) / (sin Qb)
Once you have the values for na, Qa, and Qb, simply substitute them into the equation to calculate nwater. Remember to ensure that the angles are in the same units (e.g., degrees) and that they are measured with respect to the normal to the interface between the two media.
Given that the accepted value for the index of refraction of water is 1.33, you can compare it to the calculated value to see if they align.