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624.


Problem 44.33 (RHK)


Two thin lenses of focal length and are in contact. We have to show that they are equivalent to a single thin lens with a focal length given by


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Let us consider a beam of light parallel to the common axis of the two lenses, which is incident from the left on the lens of focal length . The first lens of focal length will form a real image at its focal point, which is at a distance to the right of it. But to the second lens the rays will appear to come from a virtual object, as rays bent by the first lens enter it as though they are converging to a point to the right of the lens. Therefore, the object distance for the second lens will be . It will form an image at a distance from it. We find using the thin lens formula. We have

The image distance is positive. Therefore, the final image is real. As an incident parallel beam is focussed by the two lens combination at a distance from them, the two thin lenses in contact with each other are equivalent to a thin lens of focal length