# Glass Prism: Wavelengths

• DDV805
In summary, the problem involves finding the speed of light at a specific wavelength in a glass prism with a given index of refraction. The solution involves using a dispersion relation to find the index of refraction and then using the formula v=c/n to calculate the speed of light.

#### DDV805

Hi, could someone please help me get started on this problem. The figure is a right angle triangle with 30-60-90 degree angles (right angle). Can you help, please. Thank you so much.

The glass prism shown has an index of re-
fraction that depends on the wavelength of
the light that enters it. The index of refrac-
tion is 1.43 and wavelength 7.456 x 10-7 in vacuum and 1.61 for light of wavelength 4.951 x 10-7 m in vacuum. A beam of whitelight is incident from the left, perpendicular to the first surface, as shown in the figure,and is dispersed by the prism into its spectral components.Determine the speed of the 4.951x 10-7 mlight in the glass. Answer in units of m/s.

--------------|30
--->----------|
--------------|
--------------|90___ _60__

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If we use a dispersion relation with only two coefficients,

$$n(\lambda)=A+\frac{B}{\lambda^2}$$

we can find A and B from the input data and find n for the third wavelength. Finally,

$$v=\frac{c}{n}$$.

Hope it helps!

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oops!

I realized your "third" wavelength is identical with the second one...

I'll try to figure out another solution...

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OK, the problem seems easier than I thought:

If you have the index of refraction for a given frequency (or wavelength in vaccum) then you have the velocity from n=c/v. So, v=c/n=3e8/1.61 m/s.

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Got it.

## 1. What is a glass prism?

A glass prism is a transparent object made of glass that can refract and disperse white light into its component colors.

## 2. How does a glass prism work?

A glass prism works by refracting (bending) and dispersing white light as it passes through the prism's surface and different layers of glass. The amount of refraction depends on the wavelength of each color, causing the separation of colors.

## 3. What are wavelengths?

Wavelengths refer to the distance between two consecutive peaks or troughs of a wave. In the case of glass prisms, wavelengths refer to the different colors of light that are separated when white light passes through the prism.

## 4. How many wavelengths can a glass prism separate?

A glass prism can separate all the visible wavelengths of light, which are red, orange, yellow, green, blue, indigo, and violet. However, some prisms may be able to separate additional colors or wavelengths outside of the visible spectrum.

## 5. What are the practical applications of glass prisms?

Glass prisms have various practical applications, including optical instruments such as telescopes, microscopes, and cameras, as well as in scientific experiments and demonstrations. They are also used in rainbow makers, chandeliers, and other decorative objects.