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Convex Lenses

Convex Lenses
How does a convex lens magnify an image?
Does it always magnify?
To find out, you can draw a ray diagram to show the path of light rays through the lens.

Case 1: An Object Far From the Lens:

First, let's draw a diagram of a convex lens. This lens has two focal points, one on either side, and at equal distances from, the centre line of the lens.

Convex Lens example


Light rays from an object on one side of the lens pass through the lense and are refracted (bent). In order to see what happens to those rays of light from the object, we will look at an object sitting on the base line, far from the lens.

convex


In this first example, the object is located well outside the left focus (actually, more than twice as far from the lens as F1).
Look at the ray of light originating at the top of the object and travelling straight towards the lens. It bends as it passes through the glass, and passes through F2.

(The ray actually bends in a smooth curve inside the glass; for simplicity, we will assume it turns at some angle just as it hits the centre line).

The first principle of refraction in a convex lens is that rays of light hitting
the lens parallel to the base line will pass through the focus on the other side.


Now let's look at a second ray of light, one that leaves the top of the object and passes through F1. When it hits the lens, it will refract such that it leaves the lens parallel to the base line.

convex2


The second principle of refraction in a convex lens is that rays of light passing
through a focus and then hitting the lens will emerge parallel to the base line.


These two rays are enough to identify the location of the image. We know the image must appear to be sitting on the base line. Where the two rays intersect will be the 'top' of the image, corresponding to the top of the object.

convex3


Notice the result:
For an object far from the lens, the image
appears upside down and smaller than the object.


You can obseve this phenomenon for yourself! In a dimly lit room, turn on a light that has a single bare bulb. Hold a magnifying glass above a piece of white paper and move the paper towards or away from the magnifying glass until you see a tiny image of the light bulb appear on the paper. It will be upside down!






Case 2: An Object Closer to the Lens (But Outside F1):

Here is the lens diagram, with the object already in place, and the first ray drawn:

Convex Far away


Notice that the object is still outside F1, but within twice the focal distance. Also, when drawing the first ray of light, we followed the first principle, that a ray hitting the lens parallel to the base line will refract through the focus.

Now let's draw the second ray. It will pass through the focus on the left side first, then refract in the lens and emerge parallel to the base line.

Convex Lens Diagram 2


The point at which these two rays intersect will give us the top of the image (since the rays came from the top of the object). Here is the diagram:

Convex Lens Diagram 3


This time the image, while still inverted, is noticeably larger than the object. In other words, the object has been magnified ... its image appears bigger.

For an object located between F1 and twice the distance to F1,
the image appears upside down and larger than the object.


You can observe this phenomenon too with a magnifying glass. (Wait ... it's NOT what you think!) Again, hold the lens up so that light from the bulb passes through and onto the paper. This time, hold the lens closer to the bulb. The image appearing on the paper will again be upside down, but larger than the original bulb! Try it and see!

But this can't be what happens when you use a magnifying glass to enlarge something, because you don't see it upside down. Moreover, you seem to see the image as being on the same side of the glass as the object; both situations so far have shown an image on the opposite side of the glass as the original object. There must be another case we haven't looked at yet!