Achromatism in lenses

[Geocentric]

# 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?

 

1)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?

 

2)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?

:D 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.

[Pyrotex]

I'll check my freshman physics book tonight.