• Amith2006
In summary: Would you telling whether I am right or not?Your answers look okay to me, but again I'm no optics expert. Does your text mention the Abbe numbers that the wikipedia article uses in the achromat calculations?There is nothing given about abbe numbers in my optics book. In fact I came to know about abbe numbers from Wikipedia.
Amith2006

## Homework Statement

I posted this question in Introductory physics section but no one is able to clear my doubt. That is why I have posted it here.Please guide me.
# I have some doubts regarding achromatism of lenses:

1)If we want to form an achromatic combination of lenses in which both are made of same material, one should be convex and the other should be concave, isn’t it? Is there any other condition to be satisfied along with this?
2)It is given in a book that, a convex achromatic combination of 2 lenses of the same material placed some suitable distance is possible in the following cases:
a)Both are convex
b)Both cannot be concave
c)Convex lens of greater focal length and concave lens of smaller focal length.
Is it true?

3)A convex achromatic combination of 2 lenses of the same material placed in contact can be obtained using a convex lens of lower dispersive power and a concave lens of higher dispersive power. Is it true?

## The Attempt at a Solution

One of the reasons that you are not getting any help is that you have not shown any of your own work. What do you know about lenses? What do you know about how chromatic aberration is corrected? What is your textbook? What web resources have you tried? Have you read the wikipedia entry on chromatic aberration?

http://en.wikipedia.org/wiki/Achromat

Amith2006 said:

## Homework Statement

1)If we want to form an achromatic combination of lenses in which both are made of same material, one should be convex and the other should be concave, isn’t it? Is there any other condition to be satisfied along with this?

For the first question,I think the reason behind having one convex and other concave in order to form an achromatic doublet is that, they disperse the beam in opposite directions as one is converging and other is diverging. According to the condition for achromatism of lenses,
w1/w2 = -f1/f2
as w1 & w2 are different, f1 & f2 should be different. Is it right?

For the second question,
a) If both are made of same material, then their dispersive powers will be same. From the condition for achromatism of lenses,
f1=-f2
If both are convex, then this is not possible, isn't it?
b) Similarly both cannot be concave.
c) Similarly this cannot be true.
So for achromatism of 2 lenses made of same material placed in contact:
# one should be convex and other should be concave.
# Both should be of same focal length.

3) I think the third question is wrong because 2 lenses made of same material cannot have different dispersive powers. Please correct me if I am wrong.

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Now what is the reason for not responding?

Amith2006 said:
Now what is the reason for not responding?

Time constraints (work is extremely busy for me at the moment), and the fact that I'm not enough of an optics specialist to know the answers off the top of my head. I'd need to read the wiki article and spend some time thinking about it. What are the fundamental requirements to make an achromat? I would think it would take at least two different indices of refraction for a 2-element achromat, but I'm not sure without doing more reading.

If that is the case, I am prepared to wait. Thanks in advance.

Amith2006 said:
If that is the case, I am prepared to wait. Thanks in advance.

You shouldn't be waiting on me, Amith, or even waiting for another reply. Achromats are pretty straightforward. What have you learned about them from the wikipedia article and from your textbook?

berkeman said:
You shouldn't be waiting on me, Amith, or even waiting for another reply. Achromats are pretty straightforward. What have you learned about them from the wikipedia article and from your textbook?

Would you telling whether I am right or not?

Your answers look okay to me, but again I'm no optics expert. Does your text mention the Abbe numbers that the wikipedia article uses in the achromat calculations?

There is nothing given about abbe numbers in my optics book. In fact I came to know about abbe numbers from Wikipedia. Could anyone good in optics tell whether my resoning is right or not?

Bump!

## What is achromatism of lenses?

Achromatism of lenses refers to the ability of a lens to produce images with little to no chromatic aberration, or color distortion. This is achieved by using multiple lens elements made of different types of glass to correct for the dispersion of light.

## Why is achromatism important?

Achromatism is important in producing high-quality images with accurate colors. Without achromatism, lenses would produce images with noticeable color fringing or blurring, making them less useful for scientific and technical applications.

## How is achromatism achieved in lenses?

Achromatism is achieved by using lens elements made of different types of glass with varying refractive indexes. These elements are carefully arranged and shaped to correct for the dispersion of light, resulting in images with little to no color distortion.

## What is the difference between achromatism and apochromatism?

Achromatism corrects for two colors (red and blue) while apochromatism corrects for three colors (red, green, and blue). This means that apochromatic lenses produce images with even less color distortion than achromatic lenses.

## How can I tell if a lens is achromatic or apochromatic?

The best way to tell if a lens is achromatic or apochromatic is to check the lens specifications or consult the manufacturer. Achromatic lenses are typically labeled as "A" while apochromatic lenses are labeled as "APO". Additionally, apochromatic lenses may also be more expensive due to the use of higher quality materials.

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