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Lenses

Convex Lenses

A lens bends parallel lightrays towards and through a single point, a focus. A convex lens is one that bulges in the middle, and a concave lens is thinnest in the middle.

The large objective lens at the business end of a telescope is a convex lens. It collects a lot of parallel light from a distant object. This image may be magnified by a second lens to allow a high-resolution magnified image to be seen.

Real images

Convex lenses form real, inverted images. A real image is one which is 'really' there. To check if an image is real, place a card where the image forms. If the image appears on the card, and you don't have to look through the lens to see it, then the image is real.

Real image from a convex lens
An object outside the 2f point of a convex lens will form an inverted, smaller real image between the f and 2f point on the other side of the lens

In the case of a concave mirror, there was a point of curvature, C, which helped us determine the point where the object and image had the same size. C was two focal lengths from the mirror. A convex lens does not have a curvature point, but the same point in space, two focal lengths from the lens, we can call 2f, since f is the focal length.

Image formed by a convex lens
An object at the 2f point of a convex lens will create an image at the 2f point on the other side
Image formed by a convex lens
An object between the 2f point and the focal point of a convex lens will create an image beyond the 2f point on the other side
Virtual image with a convex lens
An object within the forcal length of a convex lens will create a virtual, upright enlarged image

The focal length, f, object distance, $d_o$, and image distance, $d_i$, are related by the same formula as for concave mirrors:

$$1/{d_o} + 1/{d_i} = 1/f$$

Magnification

The magnification of a lens can be calculated from the following formula:

$$M = f/{f - d_o} = -{d_i}/{d_o} = {h_i}/{h_o}$$

where f = focal length, $d_o$ = distance from lens to the object, $d_i$ = distance from lens to the image, $h_i$ = height of image, and $h_o$ = height of object.

The negative sign in the formula $-{d_i}/{d_o}$ indicates that the image is inverted.

Convex lens
This is a convex lens with the object inside the focal length. The result is a virtual, upright, enlarged image.
Concave lens
This is a concave lens with the object inside the focal length. The result is a virtual, upright, reduced image.

Concave Lenses

Concave lenses are shaped so they are thinnest in the middle. These lenses create a virtual, upright image on the same side of the lens as the object when viewed through the lens.

Often concave lenses are used to adjust the image and focus of telescopes and microscopes.

Virtual images

Concave lenses form virtual images. A virtual image is one which is not really there, we just think it is. For example, when we look in a plane mirror, we think we see a handsome guy (at least I do...) somewhere behind the mirror. Yet, when we look behind the mirror, he has gone away!

If you cannot see the image without looking into the mirror or lens, it is not real, only virtual. When you use a magnifying lens with only one eye, one eye sees a magnified image of the object through the glass, and the other eye, looking around the lens, sees the object with its normal size. Since we only see the image through the lens, we know it is virtual.

Concave lens
Concave lens images are always virtual, upright and reduced

Pinhole Camera

This is an example of a pinhole camera photo. Exposure for 45 seconds.

Pinhole camera image
Pinhole camera image: made from a cardboard box with a pin hole in a piece of aluminium foil, and exposing a piece of photographic paper for 45 seconds

Pinhole cameras have been used for at least a thousand years. Artists used the technique to project an image onto a screen, where it could be traced. So, how does it create an image without a mirror or a lens?

A pinhole camera is nothing more than a pinhole in a dark room or box. The origin of the word 'camera' is the Italian for 'room'. If a small hole is made in a wall, the scene outside is projected on the far inner wall of the room.

Pinhole camera image
Pinhole camera images are inverted and real

The pinhole camera has no lens. The image is inverted, and its magnification is the ratio of the image distance over the object distance.

$$M = {h_i}/{h_o} = {d_i}/{d_o}$$

Content © Andrew Bone. All rights reserved. Created : January 13, 2014 Last updated :March 5, 2016

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