Chapter 34Geometric Optics

What is Geometric Optics

It is the study of light as particles.

Geometric optics treats light as particles (or rays) that travels in straight lines.

Physical optics (wave optics) deals with the wave nature of light, such as the spreading of waves (diffraction) and the interference of waves.

Two types of lens

Converging and Diverging Lens

SymbolsConverging Lens= Convex Lens= Positive Lens

Diverging Lens= Concave Lens= Negative Lens

Some notationsF: focal pointO: objectI: image

f: focal lengthi: image distancep: object distance

Principle axis

Your textbook:f: focal lengths': image distances: object distance

Converging Lens

Converging Lens (thin)

Rules:1. Rays parallel to axisPass through focal point2. Rays through focal pointPass parallel to axis3. Rays through the centerPass through unaffected

Where is the image?

Trace at least two light rays.The image is at where the rays meet.

How to find the imageTrace two rays of light. Where they meet is where the image is.

ExampleComplete the light rays below to find the image.

Image

What if you move the object beyond 2F?

Solution

In fact all light rays from the object pass through

the image

You only need two rays to find the image

What if you now move it between F and 2F?

At F?

Between 0 and F?

DemoExploration of Physics

Summary

Real and Virtual ImageReal image can be projected directly on a screen.Virtual image cannot be projected directly on a screen without extra lenses or mirrors.

Real image forms when rays actually converge and meet.Virtual image forms when rays diverge and do not meet. Position of a virtual image is found by tracing the rays backward.

Real and virtual image

Real

Virtual

Lens Equation

Lateral Magnification

Magnification is related to i and p

Magnification is related to i and p

The sign of magnification m

Since the image is inverted, we use minus sign in front.

The sign of ii is positive if the image is on the righti is negative if the image is on the left

i >0 i<0

The sign of m

i >0, m<0, inverted i <0, m>0, upright

ExampleAssume f = 1m, complete the table below (in meters).

p i m

∞

3

2

1.5

1

0.5

SolutionAssume f = 1m, complete the table below.

p i m

∞ 1 0

3 1.5 -0.5

2 2 -1

1.5 3 -2

1 ∞ ∞

0.5 -1 +2

Diverging Lens (thin)Rules:1. Rays parallel to axisPass through focal point2. Rays through focal pointPass parallel to axis3. Rays through the centerPass through unaffected

Negative fDiverging lens obeys the lens equation too. Except that f is now negative.

2cm

Example:f =-2cm

Complete the light rays and find the

image

Solution

Different p

The typical case for concave lens

For concave lens, the image is always virtual and upright, no matter where the object is.

Can you see why i is always negative?

Example: Diverging LensYou are given a diverging lens of focal length 20cm. You

want to form an virtual image that is 1/3 the height of the object. Where should the object be placed?

Ray Diagram for the Example

Converging or diverging lens?

Converging

Converging or diverging lens? Diverging

Converging or diverging lens? Converging

Confusing signsConverging

LensDiverging

LensConverging

MirrorDiverging

Mirror

Other name ConvexLens

ConcaveLens

ConcaveMirror

ConvexMirror

f + - + -

i when image is on the left - - + +

i when image is on the right + + - -

Lensmaker’s EquationProof not required. No need to memorize, will be given in the exam. One question in Mastering Physics.R>0 if convex (bulging) toward the object.

Curved mirrors

Curved MirrorsConcave mirrorConverging mirrorPositive mirror

Convex mirrorDiverging mirrorNegative mirror

Terminology

SymbolsConverging Mirror= Concave Mirror

Diverging Mirror= Convex Mirror

Only one focal point for curved mirrors

A lens has two focal points (one on each side of the lens), but a curved mirror only has one focal point. It is important to remember where they are.Concave lens: F in front of the mirrorConvex lens: F behind the mirror

Concave Mirror Rules

F

Rules:1. Rays parallel to axisReflect through focal point2. Rays through focal pointReflect parallel to axis3. Rays through the centerReflect with equal angle

Really the same rules as converging lens

Convex Mirror Rules

F

Rules:1. Rays parallel to axisReflect through focal point2. Rays through focal pointReflect parallel to axis3. Rays through the centerReflect with equal angle

Really the same rules as diverging lens

Summary

Lens Equation applies

f is positive for concave mirrorf is negative for convex mirror

i is positive if image is in front of the mirrori is negative if image is behind the mirror

Concave mirror 1

Concave mirror 2

Concave mirror 3

Concave mirror 4

Concave mirror case 1 & 4

Convex mirrorFind the image

FVirtual image

Convex mirror

For convex mirror, the image is always virtual and upright, no matter where the object is.

Convex mirror

Multiple lensesIn the case when the first lens form a image in front of the first lens, simply treat the image as the object for the second lens.We will skip the case when the first lens gives an image behind the second lens.

Example: Image of an imageAn object 8cm high is placed 12cm to the left of a

converging lens of focal length 8cm. A second converging lens of focal length 6cm is placed 36cm to the right of the first lens. Find the position and size of the final image.

Virtual Objecthttp://science.sbcc.edu/~physics/flash/optics/virtualobject.html

p is negative for virtual objects

Confusing signsConverging

LensDiverging

LensConverging

MirrorDiverging

Mirror

Other name ConvexLens

ConcaveLens

ConcaveMirror

ConvexMirror

f + - + -

i when image is on the left - - + +

i when image is on the right + + - -

Summary

Both equations are true for lens and mirrors, but you have to be very careful about the signs!

Camera

Area of view and focal length Longer focal length, the less light is collected, need

to compensate by increasing the diameter of the aperture D. You want to keep the “f-number” f/D constant for the same intensity.

The eye

Nearsighted Eye

Farsighted eye

Microscope

Telescope

Reflecting Telescope

IQ questionA piece of glass is placed above the words “LEAD OXIDE”. LEAD appears inverted, but not oxide. Explain.