Please consider the following situations: (a) Why is it not possible to form a r

Question

Please consider the following situations:
(a) Why is it not possible to form a real image with lens C alone?
(b) If lens A and lens C were used in contact, could theyproduce a real image? Please clearly state the basis for youranswer. You will need to do a calculation.
(c) What data suggest a valid model for the equivalent focallength of two lenses in contact?
Thank you. Please consider the following situations:

(b) If lens A and lens C were used in contact, could theyproduce a real image? Please clearly state the basis for youranswer. You will need to do a calculation.
(c) What data suggest a valid model for the equivalent focallength of two lenses in contact?
Thank you.

Explanation / Answer

(a)Consider a lens having an index of refraction n and twospherical surfaces with radii of curvature R1 andR2.An object is placed at point O at a distacep1 in front of surface 1. Let's begin with the image formed by surface 1 and assumingn1 = 1 because the lens is surrounded by air,we findthat the image I1 formed by surface 1 satisfies theequation (1/p1) + (n/q1) = (n - 1/R1)-----------(1) where q1 is the position of the image formed bysurface 1.If the image is formed by surface 1 isvirtual,q1 is negative;it is positive if the image isreal. (b)Simple lenses are subject to the optical aberrationsdiscussed above. In many cases these aberrations can be compensatedfor to a great extent by using a combination of simple lenses withcomplementary aberrations. A compound lens is a collectionof simple lenses of different shapes and made of materials ofdifferent refractive indices, arranged one after the other with acommon axis. The simplest case is where lenses are placed in contact: ifthe lenses of focal lengths f1 andf2 are "thin", the combined focal lengthf of the lenses is given by (1/f) = (1/f1) + (1/f2)----------(1) Since 1/f is the power of a lens, it can be seen thatthe powers of thin lenses in contact are additive. (c)The equation (1) suggests a valid model for the equivalentfocal length of two lenses in contact. If two thin lenses are separated in air by some distanced, the focal length for the combined system is givenby (1/f) = (1/f1) + (1/f2) -(d/f1f2) The distance from the second lens to the focal point of thecombined lenses is called the back focal length(BFL). BFL = [f2 * (d - f1)/d - (f1+ f2)] As d tends to zero, the value of the BFL tends to thevalue of f given for thin lenses in contact.

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