Transcript concave mirror

Concave
(just a part of a sphere)
J.M. Gabrielse
Spherical Mirrors
(concave & convex)
J.M. Gabrielse
Concave & Convex
(just a part of a sphere)
•
C
r
•
F
f
C: the center point of the sphere
r: radius of curvature (just the radius of the sphere)
F: the focal point of the mirror (halfway between C and the mirror)
f: the focal distance, f = r/2
J.M. Gabrielse
Concave Mirrors
(caved in)
Examples include:
• Shaving and makeup
mirrors
• Inside of a metal spoon
J.M. Gabrielse
Concave Mirrors
(caved in)
•
F
optical axis
Light rays that come in parallel to the optical axis reflect through the focal point.
J.M. Gabrielse
Concave Mirrors
Because concave mirrors are curved inward they reflect light rays in
special way: reflected light rays travel toward each other, or converge.
J.M. Gabrielse
Concave Mirror
(when object is between focal point and mirror)
•
F
principal axis
J.M. Gabrielse
Concave Mirror
(when object is between focal point and mirror)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
J.M. Gabrielse
Concave Mirror
(when object is between focal point and mirror)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
J.M. Gabrielse
Concave Mirror
(when object is between focal point and mirror)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
A third ray travels to the vertex and reflects at the same angle.
J.M. Gabrielse
Concave Mirror
(when object is between focal point and mirror)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
A third ray travels to the vertex and reflects at the same angle.
A virtual image forms where the sight rays converge.
J.M. Gabrielse
Your Turn
Concave Mirror
(when object is between focal point and mirror)
•
F
object
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
Your Turn-Answer
Concave Mirror
(when object is between focal point and mirror)
•
F
object
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
Characteristics of images in Concave
Mirrors
(when an object is between the focal point and the mirror)
• S The image is larger than the object.
• P The image distance is larger than the object
distance.
• O The image is upright.
• T The image is virtual (object's image lies behind
the mirror).
J.M. Gabrielse
Concave Mirror
(when object is between the focal point and 2 times the
focal point)
•
2F
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
J.M. Gabrielse
Concave Mirror
(when object is between the focal point and 2 times the
focal point)
•
2F
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
J.M. Gabrielse
Concave Mirror
(when object is between the focal point and 2 times the
focal point)
•
2F
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
A ray travels to the vertex.
A real image forms where the light rays converge.
J.M. Gabrielse
Your Turn
Concave Mirror
(when object is between the focal point and 2 times the
focal point)
•
•
object
2F
F
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
Your Turn-Answer
Concave Mirror
(when object is between the focal point and 2 times the
focal point)
•
•
object
2F
F
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
b
Image:
S
P
O
T
Size – larger or smaller?
Position - distance?
Orientation- upside down?
Type- real or virtual?
J.M. Gabrielse
Characteristics of Images in Concave
Mirrors
(when object is between the focal point and 2 times the
focal point)
• S The image is larger than the object.
• P The image distance is larger than the
object distance.
• O The image is inverted.
• T The image is real (located in front of
mirror)
J.M. Gabrielse
Concave Mirror
(when object is beyond 2 times the focal point)
•
F
principal axis
J.M. Gabrielse
Concave Mirror
(when object is beyond 2 times the focal point)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
J.M. Gabrielse
Concave Mirror
(when object is beyond 2 times the focal point)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
J.M. Gabrielse
Concave Mirror
(when object is beyond 2 times the focal point)
•
F
principal axis
The first ray comes in parallel to the principal axis and reflects through the focal point.
The second ray comes through the focal point and reflects parallel to the principal axis.
A real image forms where the light rays converge.
J.M. Gabrielse
Your Turn
Concave Mirror
(when object is beyond 2 times the focal point)
object
•
F
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
Your Turn-Answer
(Concave Mirror)
(when object is beyond 2 times the focal point)
object
•
F
principal axis
concave mirror
• Note: mirrors are thin enough that you just draw a line to represent the mirror
• Locate the image of the arrow
J.M. Gabrielse
Characteristics of Images in Concave
Mirrors
(when object is beyond 2 times the focal point)
• S The image is smaller than the object.
• P The image distance is smaller than the
object distance.
• O The image is inverted.
• T The image is real (located in front of
mirror).
J.M. Gabrielse
Interactive Activity
See the effects of moving the object closer to the mirror,
first between the center of curvature and the focal point,
and then between the focal point and the mirror surface
(to form a virtual image):
• http://micro.magnet.fsu.edu/primer/java/mirrors/concave
mirrors/index.html
See how moving the object farther away from the center
of curvature affects the size of the real image formed by
the mirror:
• http://micro.magnet.fsu.edu/primer/java/mirrors/concave
mirrors3d/index.html
J.M. Gabrielse
Can You Name Some Other
Examples of Concave Mirrors?
Other examples of concave mirrors include:
• spotlights,
• flashlights,
• overhead projectors,
• car headlights, and
• lighthouses.
J.M. Gabrielse
More Examples
• The largest telescopes all use
concave mirrors to collect
light because the mirror
concentrates the light so
effectively.
•Satellite dishes that receive
television signals are curved
dishes that reflect the
microwaves coming from
satellites.
J.M. Gabrielse