Real world optical systems, such as telescopes or microscopes, use multiple lens

Question

Real world optical systems, such as telescopes or microscopes, use multiple lenses. In the case of the two-lens system shown here, the image I1 of the object O1 generated by the first lens (L1) becomes the object O2 for the second lens (L2). The object is 40 cm from the first lens.

1)To the nearest whole number in centimeters, where will the second image (generated by L2) be located relative to L2? Again, the image due to L1 becomes the object of L2 and a positive number means to the right, negative to the left.

2)To two decimal places, what is the magnification of the second image, the one produced by L2?

3)What is the total magnification of this optical system? (Please, explain your reasoning).

4)Construct a ray diagram for the two-lens system, showing both images (the image for L1 and the final image).

Please explain and show all your work! Thank you.

Explanation / Answer

For First image

=>   1/v = 1/15 - 1/40

=>   v =    24   cm

=>     image 1 is formed at 24 cm   to right from lens L1 .

=>   magnification m1 = -24/40 = - 0.6

For second image

=>    1/v = 1/15 - 1/6

=>   v =    - 10 cm

=>    image 2 is formed at 10 cm to the left of lens L2 .

=>    magnification m2 =   10/6 =   1.67

=>    total magnification of this optical system = m1 * m2 = - 0.6 * 1.67 =   -1

=>    Final image is same size of object but inverted .

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