Calculating Refractive Power of Two Lenses Combination

In summary, the conversation discusses the problem of finding the refractive power of a combination of two converging lenses with focal lengths of 10 cm and 20 cm placed 30 cm apart. The advice given is to use the image formed by the first lens as the object position for the second lens and apply the Gaussian lens formula to find the final image position. After some initial confusion, the individual is able to solve the problem with the help given.
  • #1
snnicols
3
0
hey- I've been working on this one for quite some time now and just can't seem to get it:
Two converging lenses with focal lengths 10 cm and 20 cm are placed 30 cm apart. Rays from a very distant object are impinged on the lens system parallel to the principal axis.
What is the refractive power of the combination of these two lenses?

it offers this help:
Look at your ray diagram. Suppose you replaced the two-lens combination with one lens that focused the incoming parallel rays the same distance away. The focal length f of the replacement lens is how far away it focuses incoming parallel rays, and the refractive power is 1/f !

i have tried everything i know how to with the given numbers...
thank you for your help!
-shawna
 
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  • #2
First, you should probably try to find where the image appears. Since the object is "very distant," you can approximate that the incident rays are parallel. Use the image formed by the first lens as the object position for the second lens and apply the Gaussian lens formula (assuming thin lenses) to find the final image position. If you can't figure out how to get the refractive power from there, post your work and we'll give some more help.
 
  • #3
but what am i supposed to use for the object distance??

i don't even know where to start, really...

using: 1/p+1/q=1/f i don't know how to find any of the variables, for object distance, image distance, and then the focal length...
i guess i don't understand what you are saying, sorry.
 
  • #4
Well, you have two lenses.

Say the parallel rays are incident on the lens of focal length 10cm from the left. This just produces an image 10cm from the right of that lens, and thus 20cm to the left of the second lens. Use the 20cm as the "object" distance for the second lens (note that the rays from the first lens converge to the focal point and then diverge again before they hit the second lens, so it's exactly like you had just placed an object at the first lens' focal point), and just apply the Gaussian formula as you would for any thin lens to see where the final image appears (you are given the focal length of the second lens).
 
  • #5
i got the answer, Data, thank you...
0.
those tricky profs sometimes, I'm sure they get a kick outta kids like me stressing out about this.
thank you again!
-shawna
 
  • #6
Very good :)
 

1. How do you calculate the refractive power of two lenses in combination?

The refractive power of two lenses in combination can be calculated by multiplying the refractive power of each individual lens. For example, if you have a lens with a refractive power of +2.00 diopters and another lens with a refractive power of -1.50 diopters, the combined refractive power would be +2.00 x (-1.50) = -3.00 diopters.

2. What is the unit of measurement for refractive power?

The unit of measurement for refractive power is diopters (D). This unit measures the strength of the lens in bending light and is equivalent to the reciprocal of the focal length in meters.

3. How does the refractive power of two lenses affect the overall strength?

The refractive power of two lenses combined will have a stronger or weaker effect on bending light depending on whether the lenses have the same or opposite signs. If the lenses have the same sign (+ or -), the overall strength will be stronger. If the lenses have opposite signs, the overall strength will be weaker.

4. Can the refractive power of two lenses be added together to get the combined power?

No, the refractive power of two lenses cannot simply be added together to get the combined power. This is because the refractive power of lenses is measured in diopters, which is a unit used for adding distances, not powers. Instead, the powers of the lenses must be multiplied together to get the combined power.

5. How does the distance between two lenses affect the refractive power of the combination?

The distance between two lenses does not affect the refractive power of the combination. The refractive power of the combination is solely determined by the individual refractive powers of the lenses and their distance from each other does not impact this. However, the distance between lenses may affect their optical properties, such as the magnification or distortion of images, which can indirectly affect the overall strength of the combination.

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