As shown in figure 24.38, an object is placed to the left of two converging lens

Question

As shown in figure 24.38, an object is placed to the left of two converging lenses. Lens 1 has a focal length f and lens 2 has a focal length 2f. The lenses are separated by a distance of 6f. An object of height h is then placed a distance of 2f to the left of lens 1. Calculate the following quantities in terms of f and h (specify the positions relative to lens 2); the position of the image produced by lens 1; the position of the final image produced by the combination of lenses; the magnification of the lens combination; the height and orientation (upright or inverted) of final image. SET UP Sketch the lens and indicate the focal points of each lens. Write down the thin-equation for lenses 1 and 2. Write down the magnification equation. Identify the appropriate object distance for lens 2, assuming that the image of lens 1 will as serve as the object for lends 2. SOLVE Use principal rays to determine the image formed by the lens. Determine the image formed by the lens. Determine the final image position. Determine the total magnification, which will he the product of the individual magnifications. Reflect Does your graphical determination of the final image agree with your calculation? Does the principal-ray diagram give the proper magnification? Where would the final image be if the Ienses were separated by 4f? Where would the final image be if the lenses were separated by 3f?

Explanation / Answer

a) f1 = f

u = - 2f

1/v - 1/u = 1/f

1/v - 1/ -2f = 1/f

v = 2f. So the image is 6f - 2f = 4f from lens 2 (Ans)

m = v/u = 2f/ -2f = -1

So the image is inverted and of the same size

b) f2 = 2f ; u = -4f

1/v - 1/u = 1/f

1/v - 1/ -4f = 1/2f

v = 4f ( Ans ) So the image is 4f right of the second lens

m = v/u = -4f/4f = -1

So image is of same size but inverted wrt to first image

c) Total magnication = magnification of 1 * magnification of 2 = -1 * -1 = 1

d) Image is upright and of the same size with respect to the object

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