Ray Diagrams. Images, Mirrors

Objectives:
To draw ray diagrams
To see how real and virtual images are formed
To use different object distances and focal lengths to create different sized images
To gain a working knowledge of the terms: real image, virtual image, upright, inverted, magnified and diminished.

Real or Virtual Images
Real Images are formed when light ray do come together to form an image.
Virtual images are formed when light rays seem to come together to form an image.
Sight lines are extensions of light rays needed to show the perceived virtual image.
Sight lines are dashed lines in ray diagrams.

Symbols Used

Plane Mirrors
(flat mirrors)
How do we see images in mirrors?

Plane Mirrors
(flat mirrors)
object
image
Light reflected off the mirror converges to form an image in the eye.
How do we see images in mirrors?

Plane Mirrors
(flat mirrors)
object
image
Light reflected off the mirror converges to form an image in the eye.
The eye perceives light rays as if they came through the mirror.
Imaginary light rays extended behind mirrors are called sight lines.
How do we see images in mirrors?

Plane Mirrors
(flat mirrors)
object
image
Light reflected off the mirror converges to form an image in the eye.
The eye perceives light rays as if they came through the mirror.
Imaginary light rays extended behind mirrors are called sight lines.
Image is virtual since it is formed by imaginary sight lines, not real light rays.
How do we see images in mirrors?

Spherical Mirrors
(concave & convex)

Concave & Convex Mirrors
are part of a sphere
C: the center point of the sphere
r: radius of curvature = the radius of the sphere
F: focal point is halfway between C and the mirror
f: the focal distance, f = r/2
f
•
C
•
F

Concave Mirrors
(caved in)
•
F
Light rays that come in parallel to the optical axis reflect through the focal point.

Concave Mirror
(Object distance: do > df)
•
F

Concave Mirror
(Object distance: do > df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.

Concave Mirror
(Object distance: do > df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.

Concave Mirror
(Object distance: do > df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
A real, inverted, diminished image forms where the light rays converge.

Concave Mirror
(Object distance: do < df)
•
F

Concave Mirror
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.

Concave Mirror
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.

Concave Mirror
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The image forms where the rays converge. But they don’t seem to converge.

Concave Mirror
Extend light rays with dashed sight lines
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
A virtual, upright, magnified image forms where the sight rays converge.

Your Turn
(Object distance do > 2df)
•
F
object
concave mirror
Note: mirrors are thin enough that you just draw a line to represent the mirror
Locate the image of the arrow

Your Turn
(Object distance: do > 2df)
•
F
object
concave mirror
Note: mirrors are thin enough that you just draw a line to represent the mirror
Locate the image of the arrow
A real, inverted same size image is formed.

Convex Mirrors
(curved out)
Light rays that come in parallel to the optical axis reflect from the focal point.
•
F
The focal point is considered virtual since sight lines, not light rays, go through it.

Convex Mirror
(Object distance do > 2df)
•
F

Convex Mirror
(Object distance: do > 2df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.

Convex Mirror
(Object distance: do > 2df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.

Convex Mirror
(Object distance: do > 2df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The light rays don’t converge, but the sight lines do.

Convex Mirror
(Object distance: do > 2df)
•
F
The first ray comes in parallel to the optical axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the optical axis.
The light rays don’t converge, but the sight lines do.
A virtual, upright, diminished image forms where the sight lines converge.

Your Turn
(Convex Mirror)
•
F
Note: mirrors are thin enough that you just draw a line to represent the mirror
Locate the image of the arrow
convex mirror

Your Turn
(Convex Mirror)
•
F
Note: mirrors are thin enough that you just draw a line to represent the mirror
Locate the image of the arrow
convex mirror
image

Lensmaker’s Equation
ƒ = focal length
do = object distance
di = image distance
if distance is negative the image is behind the mirror

Magnification Equation
m = magnification
hi = image height
ho = object height
If height is negative the image is upside down
if the magnification is negative
the image is inverted (upside down)

Refraction
(bending light)
Refraction is when light bends as it passes from one medium into another.
When light traveling through air passes into the glass block it is refracted towards the normal.
When light passes back out of the glass into the air, it is refracted away from the normal.
Since light refracts when it changes mediums it can be aimed. Lenses are shaped so light is aimed at a focal point.

Lenses
The first telescope, designed and built by Galileo, used lenses to focus light from faraway objects, into Galileo’s eye. His telescope consisted of a concave lens and a convex lens.
Light rays are always refracted (bent) towards the thickest part of the lens.
convex lens
concave lens
light from object

Concave Lenses
Concave lenses are thin in the middle and make light rays diverge (spread out).
If the rays of light are traced back (dashed sight lines), they all intersect at the focal point (F) behind the lens.

•
F
Light rays that come in parallel to the optical axis diverge from the focal point.
Concave Lenses
The light rays behave the same way if we ignore the thickness of the lens.

Concave Lenses
•
F
Light rays that come in parallel to the optical axis still diverge from the focal point.

Concave Lens
(Object distance: do < df)
The first ray comes in parallel to the optical axis and refracts from the focal point.
•
F

Concave Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.

Concave Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.
The light rays don’t converge, but the sight lines do.

Concave Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts from the focal point.
The second ray goes straight through the center of the lens.
The light rays don’t converge, but the sight lines do.
A virtual, upright, diminished image forms where the sight lines converge.

Your Turn
(Object distance: do > 2df)
•
F
Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
concave lens

Your Turn
(Object distance: do > 2df)
•
F
Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
concave lens
image
A virtual, upright, diminished image forms where the sight lines converge.

Convex Lenses
Convex lenses are thicker in the middle and focus light rays to a focal point in front of the lens.
The focal length of the lens is the distance between the center of the lens and the point where the light rays are focused.

Convex Lenses
•
F

Convex Lenses
Light rays that come in parallel to the optical axis converge at the focal point.
•
F

Convex Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts through the focal point.

Convex Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.

Convex Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.
The light rays don’t converge, but the sight lines do.

Convex Lens
(Object distance: do < df)
•
F
The first ray comes in parallel to the optical axis and refracts through the focal point.
The second ray goes straight through the center of the lens.
The light rays don’t converge, but the sight lines do.
A virtual, upright, magnified image forms where the sight lines converge.

optical axis
Your Turn
(Object distance: do > 2df)
•
F
Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
convex lens

optical axis
Your Turn
(Object distance: do > 2df)
•
F
Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
convex lens

optical axis
Your Turn
(Object distance: do = 2df)
•
F
Note: lenses are thin enough that you just draw a line to represent the lens.
Locate the image of the arrow.
convex lens
image
A real, inverted, same size image forms where the light rays converge.