Simple lens equation problem

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In summary, the converging lens would need to be placed at 10 cm from the object to produce a focused image on the screen.
  • #1
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I'm having a little problem with this question.. my brain is too small.

"A converging lens has a focal length of 10 cm. A screen is placed 30 cm from an object. Where should the lens be placed, in relation to the object, to produce a focused image?"

I've started with the formula

1/do + 1/di = 1/F

1/do + 1/di = 1/10

At this point I don't have a distance for do or di, because they're relative to the lens, and the lens position is the variable. Can someone push me in the right direction?
 
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  • #2
Look like you need to set up two simulataneous equations. You're written one down and you need to make use of 'A screen is placed 30 cm from an object' to find the other.
 
  • #3
How do I do that? Okay, could i solve this logically without using any equations?

I'm thinking, if the focal length is 10, and the distance is 30, then having the object at 1F and the screen at -2F would produce a focused image on the screen wouldn't it? Therefore the lens would be 10 cm right of the object and 20 cm left of the screen. Does that work? You've probably guess that I am terrible at this by now.
 
  • #4
Well the distance from the object to the lens is the object distance do and the distance from the lens to the screen is the image distance di, if the image from the object to the scree is 30cm what does this tell us about the sum of di and do.
 
  • #5
Max Eilerson said:
Well the distance from the object to the lens is the object distance do and the distance from the lens to the screen is the image distance di, if the image from the object to the scree is 30cm what does this tell us about the sum of di and do.

They equal 30. But something's not clicking, I don't know what to do with that.
 
  • #6
di + do = 30 (1)
and
1/do + 1/di = 1/10 (2)

Surely you can now solve for di and do from that.
 
  • #7
The best I can figure to do here, is assume do is 15 and di is 15 (half of 30)

Which sortof yields the right answer

1/15 + 1/15 = 0.13333

But I can also use assume di is 10 and do is 20

1/20 + 1/10 = .15

1/F = .1

So both are pretty close to .1 is the closer (first) one the right one?

All I know is that do and di will be 2 numbers that sum 30, but there's many combinations, and I don't know the method of getting the right one.
 
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  • #8
I think I've figured it out, just by looking at the problem and thinking logically.

do = 20 and di =-10 right? I don't know how to /calculate/ to get that though
 
  • #9
I've sort of led you round the houses here. The image is focused therefore the distance from the lens to the screen is?
 
  • #10
F? :P

Would 2F be in focus as well, out of curiousity?
 
  • #11
no it would be out of focus :).
 
  • #12
Okay, that simplifies things considerably, thanks man. :)
 

What is the simple lens equation?

The simple lens equation is a mathematical formula that relates the focal length, object distance, and image distance of a thin lens. It is represented as 1/f = 1/do + 1/di, where f is the focal length, do is the object distance, and di is the image distance.

How do I use the simple lens equation to solve problems?

To use the simple lens equation, you need to know the values of at least two of the variables – focal length, object distance, or image distance. You can then rearrange the equation to solve for the unknown variable. It is important to ensure that all values are in the same units before solving the equation.

What is the difference between a real and virtual image?

A real image is formed when light rays actually converge at a point and can be projected onto a screen. It is always inverted compared to the object. On the other hand, a virtual image is formed when light rays appear to converge at a point but do not actually do so. It is always upright compared to the object.

Can the simple lens equation be used for all types of lenses?

The simple lens equation is only applicable to thin lenses, which are lenses with a small thickness compared to their focal length. It does not work for thick lenses, which require more complex equations to determine their properties.

What are the limitations of the simple lens equation?

The simple lens equation assumes that light rays travel in a straight line through the lens and that the lens is thin. It also assumes that the lens is surrounded by air and that the object and image are far away from the lens. In reality, these conditions may not always be met, leading to deviations from the predictions of the simple lens equation.

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