Achromatism of Lenses: Answers to Your Questions

[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?

Homework Equations

The Attempt at a Solution

 

[berkeman]

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]

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.

 

[Amith2006]

Now what is the reason for not responding?

 

[berkeman]

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.

 

[Amith2006]

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

 

[berkeman]

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?

 

[Amith2006]

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?

 

[berkeman]

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?

 

[Amith2006]

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?

 

[Amith2006]

Bump!