Question

Consider a “system with two lenses in tandem”. Suppose that you have an object that is located P1to the left of a lens with F1 focal length. Then suppose that you have a second lens with F2 focal length, and you place this lens D downstream of the first lens. Let us say that the final image of the optical system forms Q2 past the second lens. The two lenses are one after another, or in tandem.

(a) Draw a picture of the optical system. Draw the picture to scale.

(b) Calculate the image distance (from first lens to the intermediate image) of the intermediate image, as measured from the first lens. Q1 in terms of P1, F1, and nothing else.

(c)Calculate the object distance (from intermediate image to the second lens) for the second lens. P2 in terms of D, P1, F1, and nothing else

(d) Calculate the final image distance (from second lens to the final image) for the second lens (Q2) , and show that this expression for Q2 satisfies the relation:

Q2 =F2(DP1-F1D-F1P1)/[(F1-P1)(F2-D)-F1P1] Equation 1

(e) Show also that the overall magnification of the system is M=(Q1Q2)/(P1P2)=F(F2-Q2)/[F2(F1-P1)] Equation 2

Answer 1

The answer of part (e) is wrong. The 'F' should be 'F₁'. You just go through the steps I have done and convince yourself. Don't think that the 'F' is the equivalent focal length of the two lenses, I have tried that too.