All optical devices make use of either reflection or refraction. Images are produced that can be either real or virtual. Real images can be projected on to a screen and are inverted. Virtual images cannot be projected on to a screen and are upright.

Mirrors

Plane Mirrors

Plane mirrors are flat reflective surfaces. When you stand in front of a mirror, you see an image that appears to be the same distance behind the mirror as you are in front of the mirror. The image appears to be the same size as the object and is laterally inverted. To understand lateral inversion, stand in front of a mirror and raise your right hand. Your image will raise its left hand.
 
 

We can locate the image by identifying selected reflected rays and extending them back behind the mirror. They intersect at a place that corresponds to where the virtual image would appear to be. We can do this because the brain "knows" that light travels in a straight line so it interprets the light rays as coming from behind the mirror.

Each observer is in a different position, but sees the image at the same place. Notice the image is the same distance behind the mirror as the object is in front of the mirror. It appears to be the same size as the object and is laterally inverted. Since no light actually passes through the mirror, there is no real image behind the mirror. Because the image appears behind the mirror, we refer to it as a virtual image.

If a surface is rough and not polished, diffuse reflection occurs an there will be no image.

Curved Mirrors

As we saw earlier in the wave section, waves obey the law of reflection when they strike a curved surface. Because of the curvature of the surface, each ray has a different angle of incidence and therefore will reflect in a slightly different way.

Concave mirrors are converging mirrors because they have the capacity to reflect light rays on to a focal point.
Convex mirrors are diverging mirrors because the reflected light rays spread out.

Concave Mirrors

In order to understand how a concave mirror produces images, we need to be able to draw a diagram of how incident waves are reflected. To do this we need to locate a few points to help us keep our bearings. While most concave mirrors are parabolic, we can simplify things somewhat if we assume that they are a section of a sphere.
 
 

The center of curvature (C) corresponds to the center of the sphere that the mirror was "cut" from.  The principle axis (PA) is a line drawn from the center of the mirror (vertex [V]), that passes through the center of curvature.  The focal point (F) is a point that lies exactly half way between the mirror and the center of curvature on the principle axis.  The distance between the vertex and focal point is the focal length (f)

Rules For Drawing Ray Diagrams

There are only 3 "rules" that we need to know in order to draw ray diagrams for curved mirrors. These ray diagrams help us predict where the image of an object will be.
 

1) If an incident ray is parallel to the principle axis, it will reflect through the focal point       2) If an incident ray passes through the focal point, it will reflect parallel to the principle axis.       3) If an incident ray passes through the center of curvature, it will reflect straight back.

Drawing Ray Diagrams For Concave Mirrors
 

Case 1: Object at a Distance: Image is real, at F and smaller than object       Case 2: Object Beyond C: Image is real, between  F and C and smaller than object   .Case 3: Object at C: Image is real, at C and the same size as the object

Case 4: Object Between F and C: Image is real, beyond C and magnified . . . .Case 5: Object At F: No image is formed .. . . . .   Case 6: Object Within F: Image is virtual, behind the mirror and magnified

Drawing Ray Diagrams For Convex Mirrors

Although convex mirrors do not converge light, they do form virtual images. We use essentially the same rules for ray diagrams, except we work with a virtual focal point behind the mirror. Reflected light does not pass through a focal point or center of curvature, but appears to have originated behind the mirror at the virtual focus or center of curvature.
 

1) If an incident ray is parallel to the principle axis, the reflected ray will appear to have originated from the virtual focal point.       2) A ray incident on the mirror that heads straight for the virtual focal point will reflect parallel to the principle axis.       3) A ray incident on the mirror that heads straight for the center of curvature will reflect straight back.

One example of a ray diagram is below. Notice the reflected rays are extended behind the mirror until they intersect. This is where the virtual image appears. It will always be smaller than the object.

The Mirror Equation

While ray diagrams work well for getting an idea of how images are formed and where they will be located, it is hard to be accurate. The mirror equation allows us to be more quantitative in locating the image. The equation is:

                                                                                1   =    1     +    1
                                                                                f         do         di

In the above equation
f = focal length,
do = distance of object from mirror,
di = distance of image from mirror.

The mirror equation works for both concave and convex mirrors. The convention is that if it is a convex mirror, the virtual focal length is negative. If di comes out negative, the image is virtual and is behind the mirror. All real images have a positive do.

Lenses

While lenses work by refracting light, you'll notice that the ray diagrams follow similar rules and that the Lens Equation is the same as the Mirror Equation. There are also two main kinds of lenses. They are converging lens and diverging lenses.
 

Converging Lens The converging lens is always "fatter" in the middle than at the ends.   Diverging lens The diverging lens is always thinner in the middle than the ends.

Converging Lenses

In order to understand how a converging lens produces images, we need to be able to draw a diagram of how incident waves are refracted. To do this we need to locate a few points to help us keep our bearings.
 
 

The principle axis (PA) is a line drawn from the center of the lens (Optical Center [O]), that passes through the focal point.  The focal point (F) is a point where the refracted rays converge when the incident rays are parallel to the principle axis. The point 2F is where the center of curvature of the lens appears to be. The optical center is where the principle axis intersects center of the lens. The distance between the vertex and focal point is the focal length (f)

Rules For Drawing Ray Diagrams

There are only 3 "rules" that we need to know in order to draw ray diagrams for  lenses. These ray diagrams help us predict where the image of an object will be.
 

1) If an incident ray is parallel to the principle axis, it will refract through the focal point     2) If an incident ray passes through the focal point, it will refract parallel to the principle axis.     3) If an incident ray passes through the optical center center, it will pass straight through.

Drawing Ray Diagrams For Converging Lenses
 

Case 1: Object at a Distance: Image is real, at F and smaller than object Case 2: Object Beyond 2F: Image is real, between  F and 2F and smaller than object Case 3: Object at 2F: Image is real, at 2F and the same size as the object

Case 4: Object Between F and 2F: Image is real, beyond 2F and magnified     Case 5: Object At F: No image is formed Case 6: Object Within F: Image is virtual, on the same side of the lens as the object.

Drawing Ray Diagrams For Diverging lenses

Although diverging lenses do not converge light, they do form virtual images. We use essentially the same rules for ray diagrams. Refracted light does not pass through a focal point or center of curvature, but appears to have originated behind the lens at F or 2F.
 

1) If an incident ray is parallel to the principle axis, the refracted ray will appear to have originated from the focal point.   2) A ray incident to the lens that passes through the optical center continues straight through

One example of a ray diagram is below. Notice the reflected rays are extended behind the mirror until they intersect. This is where the virtual image appears. It will always be smaller than the object.

Lens Equation

As with curved mirrors, ray diagrams with lenses give us a good qualitative feel about the nature of the image formed. We can be more quantitative by using the Lens equation:

                                                                               1   =    1     +    1
                                                                                f         do         di
 

Optical Instruments

The Camera
 

When the object position changes, the image position will also change, resulting in a blurry image on the film. In order to keep a clear image, we must change the position of the lens. This is accomplished when you focus the image. We can see from the lens equation that if do increases, do must decrease and vice versa. In some cases, we can replace the lens with another with a different focal length.

The Eye
 

Unlike the camera, the lens of the eye cannot move appreciably so the image cannot be focused like a camera. The eye focuses the image by changing the shape of the lens, thereby changing the focal length of the lens. We can better understand it if we solve the lens equation for 1 / di.                                        1   =    1     -    1                                        di         f          do If the object position increases, the focal length of the lens must also increase. This is accomplished by the ciliary muscles stretching the lens out to make it thinner. When you read a book, do is small, so f must also be small. This is accomplished by relaxing the ciliary muscles, allowing the lens to be more rounded.

Telescopes and Microscopes

Both telescopes and microscopes use a combination of lenses to magnify the image of an object. The eyepiece is the lens you look into. The objective is the lens that is closest to the object at which you look.
 
 

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