Question

What assumptions or approximations, if any, have been made in the Snell’s law technique? Do you think it/they were reasonable ones? Support your answer quantitatively.

Answer 1

Snell’s law approximations include treating air's index of refraction as 1 and using the small-angle approximation where sin θ ≈ θ. These are generally acceptable and result in minimal errors under standard conditions.

Step-by-step explanation:

The question pertains to the assumptions or approximations made in the application of Snell’s law. Snell's law, which is n₁ sin θ1 = n₂ sin θ2, indicates the relationship between the angles of incidence (θ1) and refraction (θ2), and the indices of refraction (n₁ and n₂) of two media. The primary approximation in applying Snell's law is the assumption that the index of refraction for air is 1. This is a reasonable approximation since the actual value up to four significant figures is very close to 1.000. Another assumption, particularly when using the small-angle approximation, is that sin θ ≈ θ, which is commonly valid for small angles measured in radians.

In cases where precision is crucial, and the angle of incidence is not small, or if the true index of refraction of air differs significantly from unity due to conditions like extreme atmospheric pressure or humidity, these approximations may introduce errors. However, under standard conditions and for educational purposes, these approximations are generally deemed to be reasonable and cause negligible errors in calculations.

Answer 2

Snell's law technique makes several assumptions and approximations, including the assumption that the incident and refracted rays are parallel, the speed of light is constant in each medium, and the medium boundaries are flat and smooth. These assumptions are generally reasonable and supported by observations and experiments.

Step-by-step explanation:

Snell's law technique makes several assumptions and approximations. The major assumptions are:

1. The incident and refracted rays are parallel to each other. This is a reasonable assumption when dealing with a medium boundary that is significantly larger than the wavelength of light.
2. The speed of light in each medium is constant and does not depend on the angle of incidence. This assumption works well for most practical scenarios.
3. The medium boundaries are flat and smooth. This assumption neglects any surface irregularities that might cause additional scattering or reflection of light.

Quantitatively, these assumptions are reasonable because they are based on observations and experiments that have been tested and give accurate results within a certain range of conditions. However, they may not hold in extreme cases or for highly irregular or non-uniform media.