## Convex Lenses

The idea of diverging and converging bundles of rays, as created by lenses, is also related to the concept of **intensity** which we encountered earlier. Recall that the intensity of an electromagnetic wave decreases as we move away from the source. This is because the energy in the wave gets "**diluted**" over a larger area.

Compare this to the light rays fanning out from a point-like source in geometric optics. Here it is the density of the rays that gets diluted. So there is a correspondence between the density of rays and the intensity of the light. Converging a bundle of rays onto a **focal point** is the same as increasing the intensity of the light.

We use the shape and material of the lens to determine its **focal point**, not by the way we send in the light rays. The distance of the focal point from the lens is not the same as the distance at which the image of a given object forms. That depends on how far away the object is. Equations that relate the distance of the object and the distance at which the image forms can be given in especially simple form if you assume that the lens is very thin.

Watch this video, which illustrates the geometric constructions behind the **thin-lens approximation**. All the constructions are drawn with a **horizontal axis** that goes straight through the center of the lens, while the lens itself is drawn vertically upright. We call the axis in this drawing the **optical axis**. For **symmetric lenses** of the type we are considering here, a light ray coming in precisely on the optical axis would hit all the interfaces between glass and air in a perpendicular direction. That would mean the ray would not change its direction because it will not experience any refraction.

Source: Khan Academy, https://youtu.be/K0sjZ5nqQ7g

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