Final answer:
Information provided is used to apply Snell's law to calculate the refractive index, and equations relating to the speed of light, its frequency and wavelength are used to find other properties of light in the syrup solution.
Step-by-step explanation:
In physics, the index of refraction 'n' of a medium can be found using 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 velocity of light in the first medium to the velocity of light in the second medium, or equivalently, to the ratio of wavelength in the first medium to the wavelength in the second medium.
(a) In this case, the first medium is air, and we can assume its refractive index to be 1. Therefore, we can calculate the refractive index for the syrup solution (n2) by rearranging Snell's law: n2 = n1 (sin θ1 / sin θ2). This gives n2 = 1 * (sin 31.4° / sin 19.3°).
(b) The wavelength λ' of light in a medium is given by λ' = λ0 / n, where λ0 is the initial wavelength in vacuum and n is the refractive index of the medium. Therefore, the wavelength of the light in the solution would be λ' = 632.8 nm / n.
(c) The frequency 'f' of the light does not change upon entering a different medium, so, it is the same as in the vacuum. Therefore, it can be calculated by using the speed of light 'c' in vacuum and the initial wavelength: f = c / λ0.
(d) The speed 'v' of light in a medium is given by v = c / n, where 'c' is the speed of light in vacuum, and 'n' is the refractive index of the medium.
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