Light and Geometric Optics

Images in Lenses

How to Locate the Image in a Converging Lens

3 Rules

A ray parallel to the principal axis is
refracted through the principal focus

A ray through the secondary principal focus
is refracted parallel to the principal axis.

A ray through the optical center continues
straight through without being refracted.

How to Locate the Image in a Diverging Lens

3 Rules

A ray parallel to the principal axis is refracted
as if it had come through the principal focus.

A ray that appears to pass through the secondary principal focus is refracted parallel to the principal axis.

A ray through the optical center continues
straight through without being refracted

Converging Lens

A lens that is thickest in the middle and that
causes incident parallel light rays to converge through
a single point after refraction

Diverging Lens

A lens that is thinnest in the middle and that
causes incident parallel light rays to spread apart after refraction

The Human Eye

Parts of the Eye

Iris

Colored part of the eye that opens and closes
to let in more or less light.

Pupil

Where light enters the eye.

Cornea

Light is refracted through the cornea.

Retina

Converts light signals into electrical signs that is
then transmitted to the brain through the optic nerve.

Optic Nerve

The optic nerve transmits electric signals from the
retina, and creates a blind spot in the back of each eye.

Focusing Problems

Hyperopia

The inability of the eye to focus light from
near objects.

Presbyopia

A form of far-sightedness caused by a loss
of accommodation as a person ages.

Myopia

The inability of the eye to focus light from distant objects.

Equations

The Lens Equation

dᵒ = object distance and is always positive

dⁱ = image distance and is positive for real images
and negative for virtual images.

f = focal length and is positive for converging
lenses and negative for diverging lenses

Used to easily determine the image characteristics

Magnification

Used to determine the magnification of a lens
for the thin lens equation.

Definition

The bending or change in direction of light when it
travels from one medium into another

Medium

The speed of light is different depending
on the medium

Rules for Refraction

2 Rules

The incident ray and reflected ray all lie in the
same plane. The incident ray and the reflected ray are on opposite sides of the line that separates the two media.

Light bends towards the normal when the speed of light in the second medium is less than in the first medium. Light bends away from the normal when the speed of light in the second medium is greater.

The Index of Refraction

Definition

The ratio of the speed of light in a vacuum to the speed of light in a medium.

Formula

n = C/V

n = sin i/sin R

Total Internal Reflection

Definition

If you increase the angle of incidence past the Critical Angle
the refracted ray will no longer exit the medium, instead, only a reflected ray is visible.

Critical Angle

The angle of incidence that results in
an angle of refraction of 90 degrees

How to Locate Image in Mirrors

Concave

4 Rules

A light ray through the principal axis
is reflected through the focus

A light ray through the center of curvature is reflected
back onto itself. The reflected ray will return on the same path.

A ray through F will reflect parallel to the principal axis.

A ray aimed at the vertex will follow the law of reflection.

Convex

3 Rules

A ray parallel to the principal axis is reflected
as if it had come through the focus

A ray aimed at the center of curvature
is reflected back upon itself

A ray aimed at the focus is reflected
parallel to the principal axis

Convex

A mirror shaped like part of the surface
of a sphere in which the outer surface is reflective

Concave

A mirror shaped like part of the surface
of a sphere in which the inner surface is reflective

SALT

Definition

Characteristics used to describe the
properties of an image

Size

The size of the image

Attitude

Is the image upright or inverted

Location

Location of the image

Type

Type of image

Real

Image formed when light
arrives at image location

Virtual

Image formed where light does not arrive
at image location

Terminology of Mirrors

Centre of Curvature

The center of the sphere whose surface has
been used to make the mirror

Principal Axis

The line through the center of
curvature to the midpoint of the mirror

Vertex

The point where the principal axis meets the mirror

Focus

The point at which light rays parallel to the
principal axis when they are reflected off the mirror

Terminology of Reflection

Plane

Flat

Incident Ray

The incoming ray that hits a surface

Reflected Ray

The ray that bounces off a reflective
surface

Normal

The perpendicular line to a
mirror surface

Perpendicular

At right angles

Angle of Incidence

The angle between the incident
ray and the normal

Angle of Reflection

The angle between the reflected ray
and the normal

Terminology of Refraction

Angle of Refraction

The angle between the refracted ray
and the normal

Terminology of Lenses

Optical Center

Point at the exact center of the lens

Principal Focus

The point on the parallel axis where light rays
parallel to the principal axis converge after refraction

Emergent Ray

The light ray that leaves a lens after refraction

Light

Definition

Electromagnetic radiation that does not
require a medium of transmission

Production of Light

Incandescense

The production of light as
a result of high temperature

Electrical Discharge

Light production by passing an
electric current through gas

Phosphorescence

Light production through the absorption of
ultraviolet light resulting in emission of visible
light

Fluorescence

The immediate emission of light as a result of
ultraviolet light

Chemiluminescence

The production of light as a
result of a chemical reaction

Bioluminescence

The production of light in living
organisms without producing heat

Triboluminescence

The production of light as a result
of friction

Light-Emitting Diode

Light produced by an electric current
flowing in semiconductors

Speed of Light

Vacuum

3.00 X 10⁸ m/s

Law of Reflection

Angle of Incidence = Angle of Reflection

The incident ray, reflected ray, and the normal
all lie in the same plane

Specular reflection

Reflection of light off a smooth surface