A light ray of wavelength 700 . nm traveling in air (n1=1.00) is incident on a boundary with a l

step 1 In this problem we have given the web length of air is equal to 700 nm. So changing the unit I c

A light ray of wavelength 700 . nm traveling in air...

A light ray of wavelength $700 . \mathrm{nm}$ traveling in air $\left(n_{1}=1.00\right)$ is incident on a boundary with a liquid $\left(n_{2}=1.63\right)$. a) What is the frequency of the refracted ray? b) What is the speed of the refracted ray? c) What is the wavelength of the refracted ray?

A light ray of wavelength $700 . \mathrm{nm}$ traveling in air $\left(n_{1}=1.00\right)$ is incident on a boundary with a liquid $\left(n_{2}=1.63\right)$.
a) What is the frequency of the refracted ray?
b) What is the speed of the refracted ray?
c) What is the wavelength of the refracted ray?

Key Concepts

Refractive Index

The refractive index of a medium is a dimensionless number that describes how light propagates through that medium. It is defined as the ratio of the speed of light in vacuum to the speed of light in the medium. This concept is crucial for understanding how light changes speed and wavelength when it transitions between different media.

Conservation of Frequency

The conservation of frequency principle states that when light passes from one medium to another, its frequency remains unchanged. This is a key concept because it ensures that while the speed and wavelength of light may vary due to differences in the refractive indices of the media, the frequency—related to the energy of the photons—stays constant.

Speed of Light in a Medium

The speed of light in a medium is determined by the medium's refractive index and is given by the equation v = c/n, where c is the speed of light in vacuum and n is the refractive index of the medium. This concept explains why light slows down when it enters a medium with a refractive index greater than one.

Wavelength in a Medium

The wavelength of light in a medium changes in proportion to the speed of light in that medium. Since the frequency remains constant, the wavelength is determined by the relationship ? = v/f, where v is the speed of light in the medium and f is the frequency. This concept is essential to understanding the behavior of light as it refracts and propagates in different materials.

Relationship Between Speed, Frequency, and Wavelength

The fundamental relationship v = f × ? connects the speed of light (v), its frequency (f), and its wavelength (?). This equation plays a central role in wave optics and is used to derive various properties of light as it interacts with different media, including changes in speed and wavelength when refracting.

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