Principles of geometrical optics

Optics
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Princ. of Geometrical Optics
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Principles of geometrical optics

Optics is the branch of physics that studies the phenomena associated with the propagation and interaction of light with matter. In the past, it was not known what light is made of. Would it be a set of particle or a wave? We now know that light is an electromagnetic wave, but sometimes, this wave behaves like particles!

Principles of Geometrical Optics

Geometrical optics is the study of the light propagation in transparent media, and is based on the fact that light can be represented as a combination of independent beams.

Important definitions:

Beams of Light: They are lines along which the energy of the electromagnetic waves propagates. They also indicate the direction of propagation.
Point Source: It is a light source where its dimensions are negligible compared to the distances between it and the objects of interest.

Consider a screen, a punctual light source, and an opaque disc between the light and the screen. A lighted region and the projected shadow of the disc will be projected on the screen.
Extensive Source: It is one that we cannot ignore its size relative to other objects in the system of interest.

Consider a screen, a light source, and an opaque disc between the light and the screen. A lighted region and the projected shadow of the disc will not be only projected on the screen but also a penumbra.
Shadow: It is the region of a body that does not receive light when this is interposed between a puntual light source and a screen. The dark region that forms on the screen is called projected shadow.
Penumbra: When an object is interposed between one extensive light source and some screen, there is a lighter shadow region before the very dark shadow. In this case, the shadow projected on the screen will also have a lighter shadow region called projected penumbra.
Monochromatic Light (Single): It is light of a single color, or an electromagnetic wave of a single frequency.
Polychromatic Light (Composite): It is the light that results from the different color lights overlay, i.e., a sum of electromagnetic waves with different frequencies.
Light Filters: They are materials that absorb all colors, except one. They have the color they do not absorb.

Material medium

The light interacts differently with different materials and in different materials they have different behaviors:

Transparent: It allows the passage of visible light, letting us see clearly objects behind them.
Translucent: It allows the passage of visible light, but do not allow us to see clearly objects behind them.
Opaque: It does not allow the passage of visible light through them.
Homogeneous: They are those that have the same properties in all the volume.
Isotropic: They are those in which the properties are the same in all directions.

Point Objects and Point Images

We are able to see objects when the ambient light is reflected on them and the reflected light reaches our eyes, forming the object images. For this reason, we cannot see in the dark.

**The figure illustrates the vision process.** The light reflected on the butterfly lamp reaches our eyes that transmit the image to our brain.

To make the study of optics easier, we may consider that an object is a set of points that "emit" light, so the image of any object is a set of images of many different points. With this, the study is summarized: we must understand the image formation of a point object. Thus we have:

Object Point: It is the vertex of the light brush incident on the optical system. The real object point is the vertex of the divergent brush of light. The virtual point is the vertex of the converging light beams.
Point Image: We define image point as the vertex of the emerging light brush of the optical system.

The figure below illustrates different objects and images points.

**Consider some screens and images being projected** on **these screens.** The point from which the image is projected (point object, represented in yellow) and the image (point image, represented in green) can be characterized in different ways. At screen (a), is shown a real image point, which generates a real image, illustrated in (a '). At screen (b) is represented a point very far from the screen image. Let it be at infinity, this point is called improper object point. At the screen (b ') is shown the image of an improper object, which has an improper image. The screen (c) is shown a virtual image point which generates a virtual image, as shown in screen (c ').

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