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Old May 8th 2010, 11:59 AM   #1
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Two Converging Lenses

A compound microscope consists of two converging lenses. Lens 1, called the objective, is a distance 61.0 mm from lens 2, called the eyepiece. The objective is placed in between the object and the eyepiece. The objective has a focal length of 15.0 mm, and the eyepiece has a focal length of 25.5 mm. If the microscope is used to examine an object placed 24.1 mm in
front of the objective, what is the distance of the final image with respect to the eyepiece?

I used the equation 1/i + 1/d = 1/f where i is the image distance, d is the object distance, and f is the focal length. I found the image distance of the objective and used that (plus the distance from the eyepiece to the objective) as the object length for the eyepiece equation. The answer given is 130 mm to the left of the eyepiece but I keep getting numbers much smaller than that. Can someone please explain what I'm doing wrong?
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Old May 8th 2010, 11:38 PM   #2
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Show your calculations to check where you are making mistake.
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Old May 10th 2010, 01:13 PM   #3
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1/d1 + 1/i1 = 1/f1 (all calculations in mm)
=> i1 = fd/(d-f) = (15)(24.1)/(24.1-15) = about 40

Because the object is outside the focal length, the image will be on the opposite side of the objective. This means the distance from the image to the eyepiece will be 61 - 40 = 21 = d2, which places it inside the focal length of the eyepiece so i2 must be on the same side of the eyepiece as d2.

so i2 = (f2)(21)/(21 - f2) = (25.5)(21)/(21-25.5) = about (-120).

The real answer is 130, but I don't see any mistakes in my math so far. Can anyone point out what i did wrong please?
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Old May 11th 2010, 12:09 AM   #4
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I think it may because of your rounding off of the figures. I tried and got 128.22 which is closer to the given answer though i agree it is not 130.
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Old May 11th 2010, 10:27 AM   #5
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We were told to round our answers, even between steps like I did, but I did it without that and also got 128. I guess that's the only number supposed to be rounded. Thanks for looking at it.
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Old May 13th 2010, 02:17 AM   #6
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Whenever the actual rays of light that refract through the lens converge behind the lens to form an image, that type of image is called a real image. Real images can be projected onto a screen, are always inverted and reversed left-to-right. For those of you who have ever loaded a slide projector, you know that you must first flip-over and then rotate each slide to insure that the image on the screen will be correctly oriented. Since the actual rays of light passing through the lens form these real images, they are also known as "hot" images. Remember, that each ray of light is composed of photons which are packets of radiant energy. If you have ever tried to use a magnifying glass to burn a hole in a dried leaf or roast a small piece of a hot dog, then you have experienced this property of real images. You instinctively learned to place the leaf or hot dog at the principal focus of the magnifying glass' converging lens.
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