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 reflection 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 and they will all reflect to be
brought to a single point.

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 focal length is 15
cm. Determine the position and size of the
image.
INDEX OF REFRACTION
The speed of light in a vacuum is 3.0x108 m/s
 In other mediums, the speed of light is less.
 We call the ratio of the speed of light in a
vacuum to the speed of light in another
medium the index of refraction

c
n
v
MORE ABOUT THE INDEX OF REFRACTION
Can a material’s index of refraction ever be less
than 1?
 Some indices of refraction that are useful:
Air – 1.0003
Water – 1.33
Crown glass – 1.52
Lucite (Plexiglass) – 1.51
Diamond – 2.42

SNELL’S LAW
When light hits the boundary of two mediums,
some of the light is reflected and some passes
into the new medium.
 Since the ray of light will be traveling at a
different speed, its path is bent.
 This is called refraction.
 Bending Light - Index of Refraction, Light,
Snell's Law - PhET

SNELL’S LAW

As light passes from a medium with a low index
of refraction to one with a higher index, the
light ray will be refracted towards the normal.
SNELL’S LAW

As light travels from a medium with a higher
index of refraction to one with a smaller index,
the light is refracted away from the normal.
SNELL’S LAW

Remember, angle of incidence and now angle
of refraction, are both measured from the
normal
n1 sin 1  n2 sin 2
TOTAL INTERNAL REFLECTION
As light passes from one material to another
where the index of refraction is less (water into
air for example), the light bends away from the
normal.
 At a particular incident angle, the angle of
refraction will be 90 degrees.
 This is called the critical angle.

TOTAL INTERNAL REFLECTION
The incident light is at such an angle that all of
the light is reflected.
 This will only occur if n1 > n2
 Many technological usages of total internal
reflection:

 Binoculars
 Fiber
optics
 endoscopes
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.

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?