# Why Does Snell's Law Give Incorrect Results When Using Certain Formulas?

• Gajan1234
In summary, the book initially provides a formula for finding refractive index using the equation N= Sin(i)/Sin(r). However, it later introduces a different formula, NxSin(i)=NxSin(r), which should be used when three quantities are given. When attempting to use this formula, the speaker received an incorrect answer and asks for clarification. The other person explains that the second equation is incorrect and the symbols must be understood. They then provide the correct equation for Snell's law, n1sinθ1 = n2sinθ2, and explain that the three quantities can be used to solve for an unknown variable.
Gajan1234
At the start of the chapter the book told me to use this formula to find refractive index: N= Sin(i)/Sin(r)
How ever later in the section they showed me to use this formula when three quantities are given : NxSin(i)=NxSin(r)
I tried apply the same method to a question, it gave me a wrong answer. Why is it?

Your second equation is not correct. You must understand what the symbols mean. What is i? What is r? What is Nx? Then the relation between the two equations you wrote will become clear.

Thank you Chandra

Snell's law should be n1sinθ1 = n2sinθ2, where n1 is the index of refraction of the incident medium with θ1 being the angle of incidence, along with n2 as the index of refraction of the refractive medium with its angle of refraction being θ2. The three quantities you are asking about are used to find a last unknown variable, by algebraically placing the 3 known variables on one side of the = sign and solving for the other side, the unknown variable.

## 1. What is refractive index?

Refractive index, also known as index of refraction, is a measure of how much a material can bend light as it passes through it. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material.

## 2. How is refractive index related to Snell's Law?

Snell's Law is a formula that describes the relationship between the angle of incidence and the angle of refraction of a light ray passing through a boundary between two materials with different refractive indices. The law 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 the refractive indices of the two materials.

## 3. What factors affect the refractive index of a material?

The refractive index of a material depends on several factors, including the density, chemical composition, and temperature of the material. Generally, materials with higher densities and higher molecular polarizabilities have higher refractive indices. The refractive index of a material also tends to decrease as the temperature increases.

## 4. How is the refractive index measured?

The refractive index of a material can be measured using various techniques, such as refractometers, spectrophotometers, or ellipsometers. These instruments use different principles to measure the angle of refraction and calculate the refractive index of the material.

## 5. What are some practical applications of Snell's Law and refractive index?

Snell's Law and refractive index have many practical applications, including in the design of lenses for cameras and microscopes, the production of optical fibers for telecommunications, and the creation of corrective lenses for eyeglasses. They are also essential in fields such as astronomy, where they are used to study the properties of light passing through different materials in space.

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