Activity 1
Lenses and Ray Optics

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Background Information

Ray diagrams show how convex lenses form images. In the first drawing, with the rays of light from the object parallel, the object is at infinity and the image is a point at the focus of the lens.

 

 

 

As the object comes in from infinity, the image moves away from the focus (and away from the lens). When the object reaches a distance of twice the focal length, the image is also at twice the focal length and is the same size as the object. These results can be summarized in a table:

Object position	Image position
infinity (extremely far away)	the focus (f)
between infinity and 2f	between f and 2f
2f	2f
between 2f and f	between 2f and infinity

Remember that the object and image can be interchanged.

What happens if the object is brought inside the focal length? Then the convex lens becomes a magnifier. It makes an image, but not one that can be seen on a screen. This kind of image is called a virtual image. The drawing shows a magnifier.

Notice that when the rays emerging from the lens are extended backward, they meet at a point behind the lens. This is the image of the arrowhead. It is a virtual image because no there is no light at this image. There seems to be light there because when an observer sees the image, it seems to come from behind the lens and to be enlarged. A virtual image cannot be projected on a screen.

An image made on a screen is called a real image. In a real image, rays that fan out from a point on the object are brought to a focus at a point on the image. When we look at an object, the lens and cornea in the eye make a real image on the retina.

The drawing below shows a ray diagram of the image made by a convex lens. The highlighted similar triangles yield an expression between the image and object heights and distances:

 

 

 

d_o = object distance
d_i 5 image distance
h_o 5 object height
h_i 5 image height
From similar triangles,
d_o / h_o = d_i / h_i

For the ray that goes through the focus,

Solving both equations above for h⁽ⁱ⁾/h_o and
substituting (to eliminate the image heights) gives

The image and object distances enter this equation symmetrically, which expresses the idea that the image and object can be interchanged (that’s what happens if the direction of the light ray is reversed). If the object is at infinity, the image is at f, and small changes in the position of a distant object have almost no affect on the position of the image. If the object is at 2f, the image is at 2f as well. Also, as the image distance gets very large, so does the image size. This suggests that in a slide or a movie projector, the film is very close to the focus of the lens.