Geometric OpticsAP Physics BMrs. Wallace

ReflectionReflection occurs when light bounces off a

surface.There are two types of reflection

Specular reflection Off a shiny surface

Diffuse reflection Off a rough surface

Mirrors are great reflectors

Plane Mirror

shiny

+

dark

-

shiny

+

shiny

+

dark

-

dark

-

Spherical Mirrors

convex concave

Light RaysMathematical rays never bend

But light rays can, if they interact with materials!

Let’s take a closer look at a plane mirror

Plane Mirror

+ -Incident ray

Reflected ray

normal

A normal is a line that is perpendicular

to the mirror.

Ray tracingRay tracing is a method of constructing an

image using the model of light as a ray.We use ray tracing to construct optical

images produced by mirrors and lenses.Ray tracing lets us describe what happens to

the light as it interacts with a medium.

Law of Reflection

The angle of incidence of reflected light equals the angle of reflection.

r = I

Note that angles are measured relative to a normal to the mirror surface.

shiny (+) dark (-)

plane mirrorlight source

incidentray

normal

reflectedray

r

i

Optical imagesNature

real (converging rays)virtual (diverging rays)

Orientationuprightinverted

Sizetrueenlargedreduced

Ray tracing: plane mirrorConstruct the image using two rays.

+ -

object5 cm

Image-5 cm

Reflected rays are diverging.

Extend reflected

rays behind mirror.

Name the image:Virtual, upright, true size

Spherical mirrorsThere are two types of spherical mirrors

shiny shiny

concave convex

+ + --(where reflected rays go) (where reflected rays go) (dark side)(dark side)

Focal length, f, is positive Focal length, f, is negative

Parts of aSpherical Concave Mirror

Principle axis

+ -These are the

main parts of a spherical concave mirror.

The focal length is half of the radius of curvature.

The focal length is positive for this type of mirror.

R = 2f

Focusf

Center

R

Identification of the focus of a spherical concave mirror

+ -Rays parallel to the principle axis all pass through the focus for a spherical concave mirror.

Ray tracing: spherical concave mirrorThe three “principle rays” to construct an

image for a spherical concave mirror arethe p-ray, which travels parallel to the

principle axis, then reflects through focus.the f-ray, which travels through focus, then

reflects back parallel to the principle axis.the c-ray, which travels through center, then

reflects back through center.You must draw two of the three principle

rays to construct an image.

Ray tracing: spherical concave mirrorConstruct the

image for an object located outside the center of curvature.

It is only necessary to draw 2 of the three principle rays!

C F

Real, Inverted, Reduced

Image

p

f

c

C F

Real, Inverted,

True Image

Ray tracing: spherical concave mirrorConstruct

the image for an object located at the center of curvature.

Name the image.

C F

Real, Inverted, Enlarged

Image

Ray tracing: spherical concave mirrorConstruct

the image for an object located between the center of curvature and the focus.

Name the image.

C F

No image is formed.

Construct the image for an object located at the focus.

Ray tracing: spherical concave mirror

C F

Virtual, Upright,

Enlarged Image

Construct the image for an object located inside the focus.

Name the image.

Ray tracing: spherical concave mirror

Problema) Construct 2 ray diagrams to illustrate what

happens to the size of the image as an object is brought nearer to a spherical concave mirror when the object outside the focus.

b) Repeat part a) for an object which is brought nearer to the mirror but is inside the focus.

Solution a)

The image becomes larger when you move the object closer.

Solution b)

The image becomes smaller when you move the object closer.

Mirror equation #11/si + 1/so = 1/f

si: image distanceso: object distancef: focal length

Mirror equation # 2M = hi/ho = -si/so

si: image distanceso: object distancemhi: image heightho: object heightM: magnification

Sample Problem A spherical concave mirror, focal length 20 cm,

has a 5-cm high object placed 30 cm from it.a) Draw a ray diagram and construct the image.

c) Name the image

Sample Problem A spherical concave mirror, focal length 20 cm,

has a 5-cm high object placed 30 cm from it.b) Use the mirror equations to calculate

i. the position of image

ii. the magnification

iii. the size of image

Parts of aSpherical Convex Mirror

These are the main parts of a spherical convex mirror.

The focal length is half of the radius of curvature, and both are on the dark side of the mirror.

The focal length is negative for this type of mirror.

Principle axis

CenterFocus

+ -

Ray tracing: spherical convex mirror

Construct the image for an object located outside a spherical convex mirror.

Name the image.

F C

Virtual, Upright

, Reduce

d Image

Problem A spherical concave mirror, focal length 10 cm,

has a 2-cm high object placed 5 cm from it.a) Draw a ray diagram and construct the image.

Problem A spherical concave mirror, focal length 10 cm,

has a 2-cm high object placed 5 cm from it.b) Use the mirror equations to calculate

i. the position of imageii. the magnificationiii. the size of image

c) Name the image

Problem A spherical convex mirror, focal length 15 cm,

has a 4-cm high object placed 10 cm from it.b) Use the mirror equations to calculate

i. the position of imageii. the magnificationiii. the size of image

c) Name the image

SummaryConcave vs convex mirrorsConcave

Image is real when object is outside focusImage is virtual when object is inside focus

Focal length f is positive

ConvexImage is always virtual

Focal length f is negative