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.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.
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.
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.
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.
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.
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.