Geometric Optics I: Plane and Spherical Optics, Lecture notes of Optics

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Lecture 17

(Geometric Optics I

Plane and Spherical Optics)

Physics 2310-01 Spring 2020

Douglas Fields

Optics -Wikipedia

• Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light. Because light is an electromagnetic wave, other forms of electromagnetic radiation such as X-rays, microwaves, and radio waves exhibit similar properties.
• Optics began with the development of lenses by the ancient Egyptians and Mesopotamians. The earliest known lenses, made from polished crystal, often quartz, date from as early as 700 BC for Assyrian lenses such as the Layard/Nimrud lens. The ancient Romans and Greeks filled glass spheres with water to make lenses. These practical developments were followed by the development of theories of light and vision by ancient Greek and Indian philosophers, and the development of geometrical optics in the Greco-Roman world. The word optics comes from the ancient Greek word ὀπτική, meaning "appearance, look".

Virtual and Real Images

• Notice that the rays that we see form the image don’t actually pass through the image.
• In this case, the solid blue lines are the real rays, and the dotted blue lines are just the direction of the rays as we perceive them.
• This image is then a virtual image.
• Without the block of glass, the rays we see are actually tracing back to the image that we perceive.
• This image is then a real image.
• Practice will make this clearer…

Plane Mirror

• Let’s begin with a plane mirror, and a point source of light.
• Rays emanate from the point source out in all directions, but we only concern ourselves with those heading in the direction of the mirror.
• The law of reflection says that each ray striking the mirror reflects with the same angle of reflection as its angle of incidence.
• The rays are then perceived to come from a point on the other side of the mirror.
• Is this a real or virtual image?

Sign Conventions

• Now, we will want to develop a set of equations that relate things like distances to images, focal points and magnification.
• In order to do this in a consistent way, we have to set up some conventions for how we assign signs (+/-) to distances.
• These don’t really have anything to do with vectors, just relations between rays and positions: - Object distance is positive if it is on the same side (of interface) as the incoming rays, else it is negative. - Image distance is positive if it is on the same side (of interface) as the outgoing rays, else it is negative.

Extended Objects and Magnification

• One can just think of an extended object as a collection of point sources, but to tell what the image is going to look like, you generally don’t need to trace rays from every point.
• For a plane mirror, for instance, one need to only trace two rays from the tip of the object…
• The (lateral) magnification of an object is defined as the ratio of the object’s lateral size to the images lateral size:
• For a plane mirror, the magnification is 1.
• Notice, that since s = -s’:

Images as Objects

• An image can also play the

role of an object.

• You can have an image of

an image (of an image…).

• We will see more of this

when we get to thin lenses.

Mirror Symmetry

• A mirror does one important thing to the image of an object. It reverses it back to front.
• Notice that any arrow pointing in a direction in a plane parallel to the mirror has an image that points in the same direction.
• Whereas an arrow that points either towards or away from the mirror will have an image that points in its opposite direction.
• The image and object together create a bilateral symmetry (or mirror symmetry).

"Ophrys apifera (flower)" by © Hans Hillewaert /. Licensed under CCBY-SA 3.0 via Commons - https://commons.wikimedia.org/wiki/File:Ophrys_apifera_(flower).jpg#/media/File:Ophrys_apifera_(flower).jpg

Spherical Mirrors

• Keeping with that small angle

assumption , one can relate the

object distance to the image

distance and radius by:

• Again, by convention, R is

considered negative if the center

of curvature is not on the same

side as the outgoing light.

Focal Points

• If we let the object distance go to infinity, then we get plane waves (parallel rays), and the spherical mirror equations tells us that the focal point of the mirror is:
• So, we can rewrite the equation as:
• Focal point, f , is positive for concave, negative for convex.
• Notice that if you can turn the rays around…

Principle Rays

• You can get a good feel for what a piece of optics can do by tracing rays.
• Some random ray can be difficult to properly draw, but…
• There is a set of rays that are relatively straightforward.
• These are called principle rays:

Principle Rays

• You can get a good feel for what a piece of optics can do by tracing rays.
• Some random ray can be difficult to properly draw, but…
• There is a set of rays that are relatively straightforward.
• These are called principle rays: