I see you are trying to find the numbers by looking simply at the ratios of the angles. However, if we are talking about refraction of light (especially since the diagram looks like a typical ray diagram), then we need to be using refraction equations, namely using Snells law. What this law does is tell us is how much a ray of light will be refracted (or bent) when it passes from one medium to the other. Mathematically it is expressed as
n(1)sin Q(1) = n(2) sin Q(2), where n(1,2) is the refractive index of the first and second medium, and Q(1,2) are the angles of incidence and refraction (as measured from the normal of the interface).
So if we use your diagram, and have the interface as the horizontal line passing through G2 (and hence the normal is the vertical line), and if we assume that the ray of light is travelling from the direction of G1 towards G2, then we can use Snells law to calculate certain things.
This is where you will find things interesting. Lets assume that we are passing light from air into some unknown medium n(2), and use the angles to calculate the refractive index of the second medium. Typically we would use the refractive index of air as 1, but I know you like decimal places so we will use the value of air (at 0 Celsius and at 1 Atm) of n = 1.000293
So we have
n(1)sin Q(1) = n(2) sin Q(2)
1.000293 X sin(43.33) = n(2) X sin (31.95)
Thus rearranging we get
1.000293 X sin(43.33)/sin(31.95) = n(2)
hence the refractive index of the second medium is n(2) = 1.2971, Which is close to the value for ice, it is not exact. It is closer to the refractive index of ice at 0C measured at infra-red wavelengths (1250 nm) or at UV wavelengths (84.7, 135.5, and 138.7 nm). It even corresponds to some microwave wavelengths (calculated using here [www.wolframalpha.com])
Note using pure gases will not get you the desired angles as the refraction angles will be very small due to the small differences between refractive indices of each gas. You can use Snells law to verify this for yourself.
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