Download mirrors and lenses - Appoquinimink High School

GEOMETRIC OPTICS
SPHERICAL MIRRORS
Mirrors that are formed from a section of a
sphere.
 Convex: The reflection takes place on the outer
surface of the spherical shape
 Concave: The flection surface is on the inner
surface of the sphere.

OBJECTS FROM FAR AWAY
If objects are infinitely far away from a mirror
(The sun, the stars, etc), the rays would be
precisely parallel.
 The law of reflection holds for each of the
parallel rays, but they will not all reflect to be
brought to a single point.
 This causes an unfocused image.

SPHERICAL ABBERATION
ASSUMPTION FOR THIS CLASS…
We will assume that the mirror is small in
comparison to its radius of curvature.
 This way, only a small angle is made upon
reflection.
 This will cause the light to reflect at nearly in
the same point, called a focus.

PARTS OF A MIRROR RAY DIAGRAM
Principle axis: The straight line perpendicular
to the curved surface at its center.
 Focal point: The point where rays parallel to
the principle axis come to a focus.

 Image
location of an object infinitely far away.
Focal length: the distance from the focal point
to the mirror.
 Radius of curvature: the center of the sphere
the mirror is made from

3 STEPS TO A RAY DIAGRAM
FOR SPHERICAL MIRRORS

Ray 1: drawn parallel to the principle axis, and
then passes through the focal point after
reflection.
3 STEPS TO A RAY DIAGRAM
FOR SPHERICAL MIRRORS

Ray 2: drawn through F; therefore must reflect
parallel to the principle axis.
3 STEPS TO A RAY DIAGRAM
FOR SPHERICAL MIRRORS

Ray 3: Perpendicular to the mirror, passes
through the radius of curvature.
RAY DIAGRAM
SUMMARY
Ray 1 goes from object parallel to the axis and
reflects through the focal point.
 Ray 2 goes from object through focal point and
reflects parallel to the axis.
 Ray 3 goes from object, perpendicular to the
mirror, reflects back on itself through the center
of curvature.

TYPES OF IMAGES
Virtual Image: If a film or paper were placed in
the location of the image, rays would not
actually pass through this location.
 Real Image: light does pass through the
location of the image. If a film were placed at
the image position, light would be put onto the
film.

OTHER WAYS TO FIND IMAGES
We could always use ray diagrams, but
accuracy is difficult.
 Mirror equation

1 1 1
 
si s 0 f
S represents distance of image and object.
f represents the focal length.
MAGNIFICATION

Magnification is the image height divided by
the object height.
hi
si
M

Sign conventions
 Positive
h0

s0
image height means upright, negative is
inverted relative to the object.
 Positive distance is in front of the mirror, and
negative is behind the mirror.
PRACTICE #1

A 1.50 cm high diamond ring is placed 20 cm
from a concave mirror whose radius of
curvature is 30 cm. Determine the position
and size of the image.
PRACTICE #2
A 1.00 cm high object is placed 10 cm from a
concave mirror whose radius of curvature is 30
cm.
A) Draw a ray diagram to locate (approximately)
the position of the image.
B) determine the position of the image and the
magnification analytically.

PRACTICE #3
A 4 cm high object is placed 3 cm in front of a
convex mirror with a radius of curvature of 8
cm.
Create a ray diagram to find the approximate
location of the image.
Analytically determine the position and
magnification of the image.

PRACTICE #4

A convex rearview car mirror has a radius of
curvature of 40 cm. Determine the location of
the image and its magnification for an object
10.0m from the mirror.
THIN LENSES
A lens is made up of two faces that are usually
portions of a sphere.
 The two faces can be either concave or convex.
 We only use thin lenses in this class which
means that the diameter of the lens is small
compared to the radii of curvature of the two
lens surfaces.

PARTS OF A LENS
Focal point: The point in which an object at an
infinite distance from the lens is focused.
 Focal length: the distance of the focal point to
the center of the lens.

 Note
that a lens has two faces and therefore two
focal points.
TYPES OF LENSES
Converging lens: a lens that is thicker in the
center than at the edges makes parallel rays
converge to a point.
 Diverging lens: a lens that is thinner in the
center than at the edges makes parallel rays
diverge.

 The
focal point is defined as the point from which
refracted rays seem to have emerged from as a
single point.
3 STEPS TO A RAY DIAGRAM
FOR THIN LENSES

Ray 1: parallel to the axis and then refracted
through the focal point on the opposite side.
3 STEPS TO A RAY DIAGRAM
FOR THIN LENSES

Ray 2: Passes through the F’ on the same side
of the lens as the object and then goes parallel
to the axis beyond the lens.
3 STEPS TO A RAY DIAGRAM
FOR THIN LENSES

Ray 3: directed towards the very center of the
lens, and emerges the same angle as it
entered.
SUMMARY
Ray 1: leaves the top of the object going
parallel to the axis and then refracts through
the focal point.
 Ray 2: passes through F’ and leaves the lens
parallel to the axis.
 Ray 3: goes straight from the object through the
center of the lens and back out the same
angle.

REAL VS. VIRTUAL IMAGES
Notice, that in the case of a lens, the light of
the image, on the opposite side of the lens, is
able to be detected by film.
 Opposite than a mirror, a real image is on the
opposite side of the lens.
 A virtual image is on the same side of the lens.

DIVERGING LENS
ANALYTICALLY

Luckily it is the same as the mirror equations
1 1 1
 
si s 0 f
hi
si
M  
h0
s0
SIGN CONVENTIONS
The focal length is positive for converging
lenses and negative for diverging lenses.
 The object distance is positive if it is on the
side of the lens from which the light is coming
(this is usually the case, although when lenses
are used in combination, it might not be so);
otherwise, it is negative

MORE SIGN CONVENTIONS
The image distance is positive if it is on the
opposite side of the lens from where the light is
coming; if it is on the same side, then it is
negative. If the image distance is positive, then
the image is real.
 The height of the image is positive it if it is
upright.

PRACTICE #1

What is the position and the size of the image
of a large 7.6 cm high flower placed 1.0 m from
a +50 mm focal length camera lens?
PRACTICE #2

An object is placed 10 cm from a 15 cm focal
length converging lens. Determine the image
position and size analytically and using a ray
diagram.
PRACTICE #3

Where must a small insect be placed if a 25 cm
focal length diverging lens is to form a virtual
image 20 cm in front of the lens?
PRACTICE #4 (TWO-LENS SYSTEM)

Two converging lenses, with focal lengths of 20
cm and 25 cm are placed 80 cm apart. An
object is placed 60 cm in front of the first lens.
Determine the position and magnification of
the final image formed by the combination of
the two lenses.