How can I derive this relation from Snell's law?

In summary, Snell's law is a mathematical equation that relates the angle of incidence and the angle of refraction when light passes through different mediums. To use it, you will need information about the refractive indices and the angles. The formula is n<sub>1</sub>sinθ<sub>1</sub> = n<sub>2</sub>sinθ<sub>2</sub>. It can be applied to light waves and other types of waves with known refractive indices. According to Snell's law, the angles of incidence and refraction are inversely proportional. It has many practical uses such as designing eyeglasses and understanding light behavior in different materials and in meteorology.
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Ahmed1029
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Here, it's shown how white light, after passing from air to another medium, gets broken down into its constituent coloured rays. Each has its own refractive index in the medium, but it's only shown here red, blue and yellow. The auther comments on this image and says that, for small angles of incidence, the difference between the angles of refraction of blue and red is proportional to the difference of their respective indeces of refraction, which is trivially obtained from snell's law. I however can't derive this proportionality from Snell's law. Can someone help me?
 
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What have you tried?
 
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1. How do I use Snell's law to derive a relation?

To use Snell's law, you need to know the refractive indices of the two materials involved and the angle of incidence. From there, you can use the equation n1sinθ1 = n2sinθ2 to derive a relation between the angles of incidence and refraction.

2. What is Snell's law and how does it relate to deriving a relation?

Snell's law is a fundamental principle in optics that describes the relationship between the angles of incidence and refraction for light passing through two different materials. By using this law, you can derive a relation between these two angles.

3. Can Snell's law be used to derive any relation?

Snell's law can only be used to derive a relation between the angles of incidence and refraction in a given scenario. It cannot be used to derive other types of relations or equations.

4. What are the limitations of using Snell's law to derive a relation?

Snell's law assumes that the materials involved are homogeneous and isotropic, meaning that their properties do not vary with position or direction. It also assumes that the light passing through the materials is monochromatic and that the surfaces are flat. Deviations from these assumptions may affect the accuracy of the derived relation.

5. Are there any other methods for deriving a relation besides using Snell's law?

Yes, there are other methods for deriving a relation between the angles of incidence and refraction. One common method is using the principle of conservation of energy, which states that the energy of a system remains constant. This can be applied to the energy of light as it passes through different materials, leading to a derived relation.

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