# This problem is a combination of optics and derivatives

• iya
In summary, according to Cartesian second law, the formula for calculating the derivative dr/di as a function of refractive index n and sinusoidal sini is derived from the Snell-Descartes law, where sini/sinr=n. The next step is to isolate r using this law.
iya
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Homework Statement
r is the angle of incidence, i is the angle of refraction. Denote the derivative dr / di as a function containing only the refractive index n and sinusoidal sini
Relevant Equations
sini/sinr=n
According to Cartesian second law, we can get this formula. but wo don't know how to do next. because we just know the sinr and sini.

iya said:
Homework Statement:: r is the angle of incidence, i is the angle of refraction. Denote the derivative dr / di as a function containing only the refractive index n and sinusoidal sini
Relevant Equations:: sini/sinr=n

According to Cartesian second law, we can get this formula. but wo don't know how to do next. because we just know the sinr and sini.
Can you post the exact question, because what is written here is not clear at all (there is not even an actual question asked). Are they asking to calculate dr/di in terms of n and sin(i) only? Then he first step is to isolate r using the Snell-Descartes law.

## 1. What is the relationship between optics and derivatives?

The study of optics, or the behavior of light, is closely related to the use of derivatives in mathematics. Derivatives are used to describe how light behaves as it passes through different mediums, such as lenses or prisms.

## 2. How are derivatives applied to solve problems in optics?

Derivatives are used in optics to calculate the rate of change of light as it passes through different mediums. This allows scientists to predict and manipulate how light will behave in various situations, such as in lenses or mirrors.

## 3. Can derivatives be used to improve optical devices?

Yes, derivatives are often used in the design and improvement of optical devices. By understanding how light behaves through the use of derivatives, scientists can make adjustments to lenses or mirrors to improve their performance.

## 4. Are there any real-world applications of the combination of optics and derivatives?

Yes, the combination of optics and derivatives has many real-world applications. This includes the development of optical instruments such as telescopes and microscopes, as well as the design of optical systems in industries like telecommunications and medicine.

## 5. Is it necessary to have a strong understanding of derivatives to study optics?

While a strong understanding of derivatives is beneficial for studying optics, it is not always necessary. Many basic concepts in optics can be understood without a deep understanding of derivatives, but a more advanced understanding is often required for more complex problems and applications.

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