[Optics] Guide required to solve achromatism numerical.

[alexshr]

Hello guys,

First of all this is not a homework. I am preparing for my exams and this question was asked in my previous exams so I tried to solve this question myself, I have tried to solve this numerical by myself, but couldn't get the answers right. So, I am posting this question here, in hope that someone would guide me to the correct direction so that I can solve it.

This question is of achromatism and I tried to use the following relations.
<br /> 1. \frac{w1}{w2} = \frac{-f1}{f2}<br />

<br /> 2. \frac{1}{F}=\frac{1}{f1}+\frac{1}{f2}-\frac{d}{f1f2}<br />

Question: Two thin lenses of focal length f1 and f2 separated by a distance d have an equivalent focal length 50cm. The combination satisfies the condition for no chromatic aberration and minimum speherical aberration. Find the values of f1, f2 and d. Assume that both the lenses are of same material.
(Ans f1=100cm, f2=33.33 cm, d=66.67 cm)

Since question states that both lenses are of the same material I tried to use the relation f1 = f2, but that didn't give me the correct answer. Please guide me.

 

[Andy Resnick]

I am having trouble understanding your question- in eqn. 1, what are 'w1' and 'w2'? Also, it's not possible to have an achromatic lens using only 1 material, and the question states both lenses are the same material.

 

[alexshr]

w1 and w2 are the dispersive power of the lenses. The question states that The combination satisfies the condition for no chromatic aberration and minimum speherical aberration, may be I understood it wrongly as achromatism question.

@andy: Can you please guide me how this question should be approached.

Thanks in advance.

 

[jtbell]

Even though this is not literally homework (course assignment), it is a homework-type problem. Therefore it has been moved to the appropriate homework help forum.