Finding the height of an image reflected through a lens?

In summary, there are two possible locations to place the lens in order to form a well-focused image of the 2.0 m tall candle flame on the wall, given a lens with a focal length of 37 cm. The heights of the images at these locations are .65 cm and 6.2 cm, with different orientations. This can be calculated using the equation 1/f = 1/s' + 1/s, where s' is the distance between the lens and the wall and s is the distance between the lens and the candle flame. By rearranging the equation and substituting the values, the values for s and s' can be found.
  • #1
surfahgirl
4
0

Homework Statement



A 2.0--tall candle flame is 2.1 m from a wall. You happen to have a lens with a focal length of 37 cm .

How many places can you put the lens to form a well-focused image of the candle flame on the wall?

For each location, what are the height and orientation of the image?

Homework Equations



1/f=1/s'+1/s

h'=(s'/s)h

The Attempt at a Solution



So I think there are 2 places you can place the lens because s'+s=210cm and s' and s are interchangeable or something like that. I'm not quite sure though.

But then for the second part, i found the heights to be .65 and 6.2 cm but either one or both are wrong. I know I have to find the values for s and s' and I'm not quite sure how to do that. I thought s' would just be 2.1 but how can you have two values for it then?
 
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  • #2
Put s' = 210 - s and substitute it in the lens formula to find s.
 
  • #3
ah..just realized that myself.
that's so simple. i was definitely over thinking it.

thanks!
 

FAQ: Finding the height of an image reflected through a lens?

How do you find the height of an image reflected through a lens?

To find the height of an image reflected through a lens, you can use the thin lens equation: 1/u + 1/v = 1/f, where u is the object distance, v is the image distance, and f is the focal length of the lens. From this equation, you can solve for v and then use the magnification formula: m = -v/u, where m is the magnification, to find the height of the image.

What is the thin lens equation?

The thin lens equation is a mathematical equation used to relate the object distance, image distance, and focal length of a lens. It is given by 1/u + 1/v = 1/f, where u is the object distance, v is the image distance, and f is the focal length of the lens.

How does the object distance affect the height of the image?

The object distance does not directly affect the height of the image. However, it does affect the image distance and the magnification of the image. As the object distance increases, the image distance also increases, resulting in a smaller magnification and a smaller image height.

What is the difference between real and virtual images?

A real image is formed when light rays actually converge at a point, and can be projected onto a screen. On the other hand, a virtual image is formed when light rays appear to be coming from a point, but do not actually converge, and cannot be projected onto a screen. Real images are formed by concave lenses and convex mirrors, while virtual images are formed by convex lenses and concave mirrors.

How does the focal length of the lens affect the height of the image?

The focal length of the lens directly affects the height of the image. The shorter the focal length, the smaller the image height will be, and the longer the focal length, the larger the image height will be. This is because a shorter focal length results in a larger magnification, while a longer focal length results in a smaller magnification.

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