Convex Mirrors
•Center of curvature and focal point both located behind mirror
•The image for a convex mirror is always virtual and upright compared to the
object
•A convex mirror will reflect a set of parallel rays in all directions; conversely, it will
also take light from all directions and reflect it in one direction
•Used for security in stores, and is also the kind of mirror used on the passenger
side of many cars
Ray Diagram for Convex Mirror
Sign convention remains same
REMEMBER focal point, f and
radius of curvature, C will be
negative (behind mirror)
Sign Convention for Spherical Mirrors
The sign conventions for the given quantities in the mirror equation and
magnification equations are as follows:
fis + if the mirror is a concave mirror (radius of curvature = 2f, also positive)
fis - if the mirror is a convex mirror (radius of curvature = 2f, also negative)
diis + if the image is a real image and located on the object's side of the mirror.
diis - if the image is a virtual image and located behind the mirror.
hiis + if the image is an upright image (and therefore, also virtual)
hiis - if the image an inverted image (and therefore, also real)
M is + if the image is enlarged
M is - if the image is reduced
Example 25.19
A convex spherical mirror with radius of curvature of 10 cm produces a virtual
image one third the size of the object. Where is the object located?
Images formed by Refraction
Refraction is the bending of a wave when it enters a medium where it's speed is
different.
Refraction is responsible for image formation by lenses and the eye.
In this case the light from the object passes through the lens and is bent, forming an
image on the other side of the lens which is magnified and inverted.
Images formed by Refraction
Example: Looking at an object in a pool, the object will appear closer than it
actually is. This is due to the fact that light is bent when passing from water to
air, as indicated below. Note that since air is less dense than water, the light
bends away from the normal as it emerges.
Your eye doesn't know
that the light has been
refracted when it comes
from water into air, and
so thinks that it has
originated from a point
closer to the surface.
Lenses
(Remember - light
passes through lenses;
lenses can reflect or
refract light)
Double-convex lens
Is converging lens
Double-concave lens
Is diverging lens
A converging lensis a lens that converges rays of light that are traveling
parallel to its principal axis. (Relatively thick across their middle and thin at
their upper and lower edges.)
A diverging lensis a lens that diverges rays of light that are traveling parallel
to its principal axis. (Relatively thin across their middle and thick at their
upper and lower edges.)
Refraction and Converging Lenses
•If the path of several light rays through a lens is traced, each of these light rays
will intersect at a point upon refraction through the lens.
•Diagram below shows several incident rays emanating from an object
•Each incident ray will refract through the lens
•The refracted rays are intersecting is the image location (converging).
•Converging lenses can produce both real and virtual images
Here, the image is a real
image since the light rays
are actually passing
through the image location
Ray Diagrams
for
Converging
Lenses
Three rules of refraction for a double convex (converging) lens:
•Any incident ray traveling parallel to the principal axis of a converging lens will refract
through the lens and travel through the focal point on the opposite side of the lens.
•Any incident ray traveling through the focal point on the way to the lens will refract
through the lens and travel parallel to the principal axis.
•An incident ray that passes through the center of the lens will in effect continue in
the same direction that it had when it entered the lens.
Ray Diagrams for
Converging Lenses
Refraction and Diverging Lenses
•Diverging lens create virtual images since the refracted rays do not actually
converge to a point
•The image location is located on the object's side of the lens where the
refracted rays would intersect if extended backwards
•The location where the refracted rays are intersecting is the image location.
Since refracted light rays do not actually exist at the image location, the image is
said to be a virtual image.
Ray diagrams and Diverging Lenses
Three simple rules of refraction for double concave (diverging) lenses:
•Any incident ray traveling parallel to the principal axis of a diverging lens will refract
through the lens and travel in line with the focal point (i.e., in a direction such that its
extension will pass through the focal point).
•Any incident ray traveling towards the focal point on the way to the lens will refract
through the lens and travel parallel to the principal axis.
•An incident ray that passes through the center of the lens will in affect continue in
the same direction that it had when it entered the lens.
Ray diagrams and Diverging Lenses
The diagrams above show that in each case,
•the image is located on the object' side of the lens
•a virtual image
•an upright image
•reduced in size (i.e., smaller than the object)
Unlike converging lenses, diverging lenses always produce images that
share these characteristics.
Refraction from Plane
Surfaces
Rays originating at the object location are
refracted at the spherical surface and converge
at the image point.
n1 – index of refraction for 1st medium
ho – height of object
do – distance from lens surface to object
R – radius of curvature
Relating n and d(derivation
combines Snell’s law & geometry):
n1 /do + n2 /di= (n2 – n1)/R
Magnification:
M = hi /ho = - n2di/n1do
For plane surface (R = ∞):
n1 /do = - n2 /di
n2 – index of refraction for 2nd medium
hi – height of image
di – distance from lens surface to image
Sign Convention for Refracting
Surfaces
The sign conventions for the given quantities
R is + if center of curvature is in back of the surface
R is - if center of curvature is in front of the surface
dois + if the object is in front of the surface (real object)
dois - if the object is in back of the surface (virtual object)
diis + if the image is in back of the surface (real image)
diis - if the image in front of the surface (virtual image)
Sign convention for spherical refracting surfaces is the same as for
mirrors, recognizing the changes in sides of the surface for real and
virtual images.
Example 25.29
A goldfish is swimming in water inside a spherical plastic bowl of index of
refraction 1.33. If the goldfish is 10 cm from the wall of the 15-cm-radius
bowl, where does the goldfish appear to an observer outside the bowl?
Example 25.47
A diverging lens is used to form a virtual image of an object. The
object is 80 cm to the left of the les and the image is 40 cm to the left of
the lens. Determine the focal length of the lens.