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The Focal Length of a Lens
Consider light leaving a point on a source placed on the principal axis, and relatively close to a converging lens, as shown below.
The light is converged to a real image point on the axis.
 
We now move the source further from the lens, as shown in the next diagram.
If we assume that the same lens will produce the same deviation of the light, then, clearly, the rays will meet nearer to the lens than in the first case.
We therefore conclude that as the object distance increases, the image distance decreases.
This is confirmed by experiment.
 
Now imagine moving the object much further away
Imagine that the three rays on the next diagram come from a point on a source 25m away or more.
Those rays will be very nearly parallel.
Also, if the object is then moved, say, ten times further away, no change would be expected in the image distance.
Once the object is far enough for the rays to be considered parallel then the image distance will reach a fixed value.
This constant, minimum value of image distance (for a given lens), is called the focal length of the lens, f.
 
 
The point on the axis where the parallel rays meet is called the principal focus (or principal focal point), F.
 
Rays which are parallel to each other but not to the principal axis of the lens are converged to meet at other points the same perpendicular distance from the lens as the principal focus, as shown below.
These points define the focal plane of the lens.
 
The Power of a Lens
In everyday speech, if one mentions a "powerful magnifying glass" one thinks of a converging (convex) lens with strongly curved surfaces.
For example,of the two lenses shown below, the second "fatter" lens would make the better magnifying glass.
We notice that the lens with the more strongly curved surfaces has a shorter focal length.
 
We define the power of a lens as follows
where, if the focal length is in metres, the power is in Dioptres (D)
 
Thus, a converging lens of focal length 50cm has a power of 2D.
Similarly, a diverging lens of focal length 25cm, has a power of -4D (see here for explanation of the negative sign).
 
 
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