Reflection and Mirrors

Ray Model of Light Light is a particle that propagates in straight lines, unless it is reflected or enters a new medium. Pioneered by Isaac Newton in his book Opticks

Theories of Light Ray Model, Wave Model, Photon Model The Ray Model, although not perfect, explains a great deal of phenomena Reflection, refraction, mirrors, and lenses The Ray Model was the first attempt for scientists to model the behavior of light.

Light is fast! Really fast! 300,000,000 m/s 1/10th of a second to go from NY to LA 1 light year = the distance that light travels in one year The speed of light in a vacuum is the speed limit of the universe c = 3 x 108 m/s (speed of light in a vacuum)

The ray reflects symmetrically across the normal line. The Law of Reflection incident ray normal reflected ray θi θr mirror The ray reflects symmetrically across the normal line. The normal line is perpendicular to the surface of the mirror, and touches the point where the ray hits the mirror. θi = θr

Think of the mirror as a part of a circle! When the mirror is curved, the normal line is basically just the radius of the mirror. incident ray normal θi Think of the mirror as a part of a circle! mirror θr reflected ray

Ray Model of Light One of the most important components of the Ray Model is the way that objects emit light. In a well-lit room, all objects are visible from every angle. Not only this, but every point on the object is visible from all directions! This is because when objects reflect light, the light rays are so numerous that each point on the surface of the object constantly emits light in all directions. The room is completely filled with light, constantly reflecting off of objects!

Many, many rays… However, we can only detect the ones that reach our eye! In fact, there are so many rays constantly reflecting off of ordinary objects that the Ray Model assumes an essentially infinite number of light rays coming out in all directions.

Virtual Rays! mirror reflected ray virtual ray incident ray Virtual rays are a geometrical tool to show the direction that reflected rays of light appears to come from. Although virtual rays are not actual light, they will help us show where a virtual image exists. You will see that your eye (and brain) can be fooled by reflections!

Image Produced by a Plane Mirror All of the reflected rays that came from the top of the arrow appear to come from the same location behind the mirror!

Image Produced by a Plane Mirror Similarly, all of the reflected rays that came from the bottom of the arrow appear to come from another location behind the mirror! mirror

Image Produced by a Plane Mirror object virtual image

Virtual Images are Amazing Virtual image – the location where light that is reflected by the mirror appears to come from! Your eye actually sees the equivalent light as if there was a second, identical object located behind the mirror! mirror Although personal experience with mirrors and imperfections in the mirror usually give it away, your brain can be easily fooled by a mirror… virtual image

What does the image look like? The virtual image formed by a plane mirror will be The same size as the object. Equidistant from the mirror perpendicularly. Flipped left-to-right relative to the object (mirror image) d d h h object virtual image mirror

Image Produced by a Convex Mirror virtual image object

Convex Mirror The image produced by a convex mirror is virtual, upright, reduced in size, and closer to the mirror than the object! do di ho hi virtual image object convex mirror

Concave Mirrors Like a cave! principal axis This side of the mirror is shiny principal axis center of curvature Like a cave!

This type of mirror is sometimes called a converging mirror. Concave Mirrors focal point c Incoming rays that are parallel to the principal axis will all pass through the focal point! This type of mirror is sometimes called a converging mirror.

Due to its geometry, a circularly curved mirror has a focal length that is one half of its radius of curvature. f c

normal f c And don’t forget, the center of curvature will show you where to draw the normal line when a ray reflects from a curved mirror!

Now this is called the antifocal point Convex Mirrors Now this is called the antifocal point Now the outside of the mirror is shiny! f c Like a… vex…

This type of mirror is sometimes called a diverging mirror. Convex Mirrors f c Incoming rays that are parallel to the principal axis will diverge directly away from the antifocal point! This type of mirror is sometimes called a diverging mirror.

Principal Rays (or Guiding Rays) Although there are essentially an infinite number of rays emanating from the object, we can use three principal rays to help us determine the location of an image produced by a curved mirror. c f

P-Ray (Parallel Ray) Emitted by the object, traveling parallel to the principal axis. It is then reflected through the focal point! c f

P-Ray: Convex Version Emitted by the object, traveling parallel to the principal axis. It is then reflected away from the antifocal point! f c

F-Ray (Focal Ray) Emitted by the object, traveling toward the focal point. It is then reflected parallel to the principal axis! c f This is basically the inverse of the P-ray.

F-Ray: Convex Version Emitted by the object, traveling toward the antifocal point. It is then reflected parallel to the principal axis! f c

C-Ray (Center Ray) Emitted by the object, traveling toward the center of curvature. It is then reflected directly back along its original path! c f

C-Ray: Convex Version Emitted by the object, traveling toward the center of curvature. It is then reflected directly back along its original path! f c

Principal rays allow you to locate an image Any two of the principal rays will show the location of the image at the point where they intersect. However, I recommend drawing all three to be safe (and make sure that they all meet at the same point!) Try it!

c f real image

You need to see it to believe it.. Real Images Rather than a virtual image (which is formed by virtual rays), a real image is formed by real rays! It can only be produced by a concave mirror, and only if the object is further than the focal point. Since the image is formed by actual rays of light in front of the mirror, it can be projected onto a screen. You need to see it to believe it..

Concave Mirror – Object further than c Color Code P-ray F-ray C-ray c f The image is real, inverted, and reduced.

Concave Mirror – Object at c Color Code P-ray F-ray C-ray f c The image is real, inverted, and the same size as the object.

Concave Mirror – Object between c and f Color Code P-ray F-ray C-ray f c The image is real, inverted, and enlarged.

Concave Mirror – Object at focal point Color Code P-ray F-ray C-ray c f These will never intersect NO IMAGE IS FORMED!!!

Concave Mirror – Object closer than f Color Code P-ray F-ray C-ray f c The image is virtual, upright, and enlarged. This is why concave mirrors with large focal lengths are used as makeup mirrors!

Concave Mirrors: Summary Object Location Image Orientation Image Size Image Type Beyond c Inverted Reduced Real At c Same as object Between c and f Enlarged At f No image Closer than f Upright Virtual If the object is further than f, the image will be inverted and real. If the object is closer than f, the image will be upright and virtual.

Convex Mirror – Object anywhere Color Code P-ray F-ray C-ray f c The image is virtual, upright, and reduced.

Convex Mirrors: Summary Object Location Image Orientation Image Size Image Type Anywhere Upright Reduced Virtual This is why convex mirrors are used for seeing large areas at once!

Real vs Virtual Images Real images are formed by actual light rays (not virtual rays). They are able to be seen directly with the human eye, and can also be projected onto a screen! Virtual images are formed by virtual rays. A virtual image is the appearance of light originating from a certain location, although the light never actually did (it was redirected by a mirror or lens to look like it did!) When a virtual image is formed, it can be seen by the human eye. However, it cannot be projected onto a screen!