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Lens Principle

Bigshot's lens, as we saw in the Introduction, is made from several different pieces, but for simplicity's sake we can think of it as a single-piece lens.  The goal of the lens is to funnel (or converge) all the light it receives from a point outside the camera towards a specific point inside the camera.  Note that each of the incoming light rays must be bent differently in order to achieve this.   We cannot magically change the bending power of the lens's glass itself to do this, but we are able to design the shape of the lens.

Most lenses are spherical; that is, each of their surfaces is part of a sphere. Lenses that bulge outwards, such as the one in Figure 6, are called convex lenses.  This type of lens is often used in cameras because they converge light.

Convex lens
Figure 6: Convex lens

Each of the two surfaces of the convex lens in Figure 6 is part of a sphere of radius R.   The dotted line that connects the centers of these spheres is called the optical axis.   The lens converges light rays that are parallel to the optical axis towards a single point on the optical axis called the focal point. The distance between the focal point and the center of the lens is called the focal length of the lens.  It is a measure of how much the lens bends incoming light [1].  The focal length (f) depends on the curvature and refractive index (n) of the lens as shown in the equation below [1]:

Equation 1.

If each surface of the lens has its own curvature (say, R1 and R2), the lens’s focal length (f) is given by the Lensmaker's Formula [1]:

Equation 2.
References
[1] E. Hecht, Optics. Addison Wesley, 2001.

 

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