# Interference using composite lens

I encountered a question while attempting an exam. I cannot really understand how to go about it.

It is clear that the concave part forms the image at a distance $$3 \lambda /2$$ behind the lens, and the convex part forms an image at a distance $$3 \lambda /2$$ in front of it. Now, I do not understand what 'd' is supposed to be. If I assume it to be the distance at which image by convex lens is formed, I don't know what to do next. I can visualise a constructive interference happens there, but it happens only because of the rays from the convex part. So intensity should be 2I. But the answer they have given is 4I. I'll post their explanation below:

How do they correlate the distance between the images and the fact that maxima occurs at O? Thanks in advance.

• Well really the question gives no indication on d and O except that there happens to be a screen there. The intensity really should be a function of d. – Paul Childs Mar 27 at 6:48
• Yes. And in the explanation they write "d=3λ", which they assume to be the distance between images. It isn't possible, as no image forms at the pole of the lenses. The question and the answer are inconsistent. – Arka Seth Mar 27 at 6:49
• Bizarre. Usually for geometric optics I'd use the Fourier transform. In this case it comes out as $\delta(k) -\frac{i}{\pi k}$. This is in the far field though. $3 \lambda$ is near field so you'd have to run a Fresnel integral.Don't see how you can get 4I though. – Paul Childs Mar 27 at 22:03