What is the relation between the refractive index velocity of light in vacuum c and medium V )?

Refractive Index (Index of Refraction) is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. The refractive index variable is most commonly symbolized by the letter n or n' in descriptive text and mathematical equations.

As presented in the figure above, a wavefront incident upon a plane surface separating two media is refracted upon entering the second medium if the incident wave is oblique to the surface. The incident angle (θ(1)) is related to the refraction angle (θ(2)) by the simple relationship known as Snell's law:

n1 × sin(θ1) = n2 × sin(θ2)

Where n represents the refractive indices of material 1 and material 2 and θ are the angles of light traveling through these materials with respect to the normal. There are several important points that can be drawn from this equation. When n(1) is greater than n(2), the angle of refraction is always larger than the angle of incidence. Alternatively when n(2) is greater than n(1) the angle of refraction is always smaller than the angle of incidence. When the two refractive indices are equal (n(1) = n(2)), then the light is passed through without refraction.

In optical microscopy, refractive index is an important variable in calculating numerical aperture, which is a measure of the light-gathering and resolving power of an objective. In most instances, the imaging medium for microscopy is air, but high-magnification objectives often employ oil or a similar liquid between the objective front lens and the specimen to improve resolution. The numerical aperture equation is given by:

NA (numerical aperture) = n × sin(θ)

where n is the refractive index of the imaging medium and θ is the angular aperture of the objective. It is obvious from the equation that increasing the refractive index by replacing the imaging medium from air (refractive index = 1.000) with a low-dispersion oil (refractive index = 1.515) dramatically increases the numerical aperture.

Snell's law was originally defined by the relationship between the incident angles and the ratio of the velocities of light in the two media. The refractive index or index of refraction is the ratio between the velocity of light (c) in free space (for all practical purposes, either air or a vacuum) and its velocity η in a particular medium:

n = c/η

As the refractive index of a material increases, the greater the extent to which a light beam is deflected (or refracted) upon entering or leaving the material. The refractive index of a medium is dependent (to some extent) upon the frequency of light passing through, with the highest frequencies having the highest values of n. For example, in ordinary glass the refractive index for violet light is about one percent greater than that for red light. A consequence of this phenomenon is that each wavelength experiences a slightly different degree of refraction when a heterogeneous light beam containing more than one frequency enters or leaves the medium. This effect is termed dispersion and is responsible for chromatic aberration in microscope objectives.

An incandescent light bulb is shown through a glass prism. The certain wavlength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively.

The velocity of the light __________ when it moves from air to glass.

Possible Answers:

Correct answer:

decreases

Explanation:

This question asks us to consider the relationship between velocity and index of refraction of a medium. If we think back to the definition of index of refraction, we know that it is defined by the ratio of the velocity of light in a vacuum and the velocity of light in some other medium.

n is the index of refraction, c is the speed of light in a vacuum, and v is the speed of light in the new medium.

We can see that n and v are inversely proportional, meaning that the higher the n, the lower the velocity. As the light moved from air (n =1) to glass (n = 1.5), the n increased, and thus the velocity must decrease because the speed of light in a vacuum is constant.

An incandescent light bulb is shown through a glass prism. The certain wavlength of the light is then directed into a glass cuvette containing an unknown concentration of protein. Commonly, this process is called spectroscopy and is used to determine the concentrations of DNA, RNA, and proteins in solutions. The indices of reflection of air, glass, and the solution are 1, 1.5, and 1.3, respectively.

As light exits from the wall of the cuvette into the solution, its wavelength __________.

Possible Answers:

Correct answer:

increases

Explanation:

This question asks us to find the relationship between the wavelength and index of refraction. We will need to know two equations to compute the relationship between the two.

First, we need to relate velocity and index of refraction. The definition of index of refraction allows us to relate the two.

We also know the relationship between velocity and wavelength.

 We can now set these formulas equal to each other to find the relationship between wavelength and index of refraction.

We can see that

How long will it take a photon to travel 

Possible Answers:

Correct answer:

Explanation:

The index of refraction is equal to the speed of light in a medium divided by the speed of light in a vacuum.

We can find the time to travel a given distance by manipulating this equation and combining it with the equation for rate:

Plug in the given values and solve for the velocity in the medium.

Now we can return to the rate equation and solve for the time to travel

We can recognize that the answer can be simplified by converting to nanoseconds.

The refractive index of medium A is 1.2, while that of medium B is 1.36. Through which medium does light travel faster and at what speed does it travel?

The speed of light is

Possible Answers:

Medium A at velocity

Medium B at velocity

Medium A at velocity

The speed of light will be

Medium B at velocity

Correct answer:

Medium A at velocity

Explanation:

The refractive index of a medium (n) is equal to the speed of light (c) divided by the velocity of light through the medium (v).

Which of the following does not take place when a light wave travels from a medium with a high index of refraction into one with a lower index of refraction?

Possible Answers:

The light ray bends away from the normal line

The refracted light remains in phase with the incident wave

Correct answer:

Frequency increases

Explanation:

As the wave travels into the less dense medium, it speeds up, bending away from the normal line. The index of refraction tells the ratio of the velocity in a vacuum in relation to the velocity the medium; thus, the velocity will be greater in a medium with a lower index of refraction.

Frequency remains the same regardless of medium, however, since the velocity changes, the wavelength must accommodate this change.

If velocity increases and frequency remains constant, wavelength must also increase.

Finally, a phase shift only occurs when a light ray reflects from the surface of a more dense medium.

What is the index of refraction for a material in which light travels at

Possible Answers:

Such a material does not exist, since the speed of light is constant

Correct answer:

Explanation:

Relevant equations:

To find index of refraction, divide the speed of light in a vacuum by the speed of light in the material:

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