Calculating Chromatic Aberration in Dense Flint Lenses: A Homework Solution

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In summary, the conversation discusses the concept of refractive index and its effect on lenses, specifically in terms of chromatic aberration. The example of dense flint as a refractive material with varying refractive indices for different wavelengths of light is given. The conversation then poses a question about the distance between the red and blue-violet images of a white object when passing through a converging lens made of dense flint. The solution involves using the lens maker equation and the standard lens equation to calculate the focal length and image distances for both red and blue light, and then finding the difference between the two distances.
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Homework Statement



The refractive index of a material is different for different wavelengths and colours of light. For most materials in the visible range of the electromagnetic spectrum, shorter wavelengths have larger refractive index compared to longer wavelengths.

The effect of this on lenses is that different colours from one object will be focused at different distances and thus it is impossible to have the whole object completely focused. This is known as chromatic aberration.

Dense flint is a refractive material for which the shortest wavelength of the visible spectrum at violet-blue (400 nm) has a refractive index of 1.80, while for the longest wavelength of the visible spectrum at red (800 nm) has a refractive index of 1.70

Consider a converging lens made out of dense flint with R1=10 cm and R2=-10 cm.

We place a white object at a distance of 119 cm from the lens. Since white light is composed of all visible colours, when it passes through the lens, the different colours will form images at different distances.

What is distance between the red image of the object and the blue-violet image?

Homework Equations



lens maker equation

The Attempt at a Solution




The focal length at any particular wavelength can be calculated using the "lens maker's formula"

For white light with n = 1.75 (a red-blue average),
1/f = (0.75)(1/10 + 1/10) = 0.15
f(white)= 6.67 cm
f(blue) = 5/0.8 = 6.25 cm
f(red) = 5/0.7 = 7.14 cm

Use the standard lens equation
1/f = 1/do + 1/di
to compute the difference in the image distances, di. Use do = 119 cm

What is the f in the equation
 
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f is the focal length, that is the length at which a lense focuses a given object.

using the infomation given you are able to input firstly into the lensmakers equation to find a focal length and then in the standard lens equation to find the image distance for both red and blue light, which enables you to find the difference in distances

try having a look at http://hyperphysics.phy-astr.gsu.edu/Hbase/geoopt/lenseq.html#c1
 

What is a refractive material?

A refractive material is a substance that can bend or change the direction of light as it passes through it. This is due to the material's ability to slow down or speed up the light waves, causing them to change direction.

How do refractive materials work?

Refractive materials work by interacting with the photons of light that pass through them. When light enters a refractive material, it slows down and changes direction, which causes the light to bend. The amount of bending depends on the properties of the material, such as its density and composition.

What are some examples of refractive materials?

Some common examples of refractive materials include glass, water, and plastic. These materials are used in lenses for glasses, camera lenses, and magnifying glasses. Other examples include diamonds, which have a very high refractive index, and air, which has a very low refractive index.

How are refractive materials used in everyday life?

Refractive materials are used in a variety of applications in everyday life. They are essential in the production of lenses for glasses, contact lenses, and cameras. Refractive materials are also used in optical instruments such as microscopes and telescopes. In addition, they are used in the production of mirrors, prisms, and other reflective surfaces.

What is the refractive index of a material?

The refractive index of a material is a measure of how much the speed of light is reduced when passing through it. It is defined as the ratio of the speed of light in a vacuum to the speed of light in the material. The higher the refractive index, the more the light will bend as it passes through the material.

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