Reflection & Mirrors

Law of Reflection θi = θr The angle of incidence = the angle of reflection

We like smooth surfaces because the normal is easy to identify and is perfectly vertical…if the surface isn’t smooth, it gets a little more complex.

Law of reflection still applies!!Specular Reflection

Parallel light rays reflected parallel

Diffuse Reflection parallel light rays NOT reflected parallel – instead are

scattered off a rough surface

Because reflected rays are scattered from a rough surface, they

cannot be seen…this is why materials with

rough surfaces cannot be used as mirrors.

Question???

Can you see light that isn’t directed toward your eyes?

Answer

No… What you see are the reflected rays. If none

of the reflected rays are directed straight toward your eye, then you see no light.

Again, this is why we don’t see a reflection in a piece of paper…the incident rays go in parallel, but then are scattered all over. Our eyes cannot produce an image from the scattered reflected rays.

Plane Mirrors

Flat, smooth surface from which light is reflected by specular reflection.

Object – source of light (either luminous or illuminated)

Image – brain always processes information as if light has traveled in a straight path, so we don’t see the object…we see the image.

Look at figure 17-5 on page 461

Plane Mirrors

Image Position

Image Height

di = -do

hi = ho

•The object is always on the positive side of the mirror. • The image formed with a plane mirror is on the opposite side of the mirror.• We call this a virtual image, and its distance is negative.

Curved Mirrors

Convex Concave

Variables

do

di

ho

hi

Object distance- distance from the object to the mirror

Image distance- distance from the image to the mirror

Object height- how tall the object is

Image height- how tall the image is

Real Image: Formed when actual reflected or refracted rays converge; can be projected onto a screen

Virtual Image: Formed when the extended (dotted) lines converge to form the image

Concave Mirror – Edges curve toward observer

Focal Pt. (f)

Center of Curvature

Focal length

Radius of Curvature (2xFocal Length)

Principal Axis

Focal Point – point where incident light rays that are parallel to the principal axis converge after reflecting from the mirror.

Convex Mirror – Edges curve away from observer

Focal Pt. (f)

Focal Length

Center of Curvature

Radius of Curvature = 2f

Principal Axis

Graphical Method of Finding the Image -Ray Diagrams-

-Determine properties of an image formed by a curved mirror.

-Typically Given-Type of mirror-Focal Length & Center (or radius) of curvature-Object Height-Object distance

-What are we looking for??-Is the image real, or virtual?-Is the image smaller, larger, or same size?-Is the image erect or inverted?-How far is the image from the mirror? (di)

Step 1: Draw the principle axis

Step 2: Represent the kind of mirror being used.

Step 3: Show focal pt. and center of curvature

f C

Step 4: Show Object

ho

do

C = 2f

f C

Ray 1: For a convex mirror, a ray entering towards the focal point will reflect parallel to the principle axis

Convex Mirror

f =

do =

ho =

f C

Ray 2: For a convex mirror, a ray entering parallel to the principle axis will reflect in a direction that makes it appear to come from the focal point.

Convex Mirror

f =

do =

ho =

f C

Ray 3: For a convex mirror, a ray entering towards the center of curvature will reflect back upon itself, appearing to have come from the center of curvature.

Convex Mirror

f =

do =

ho =

f C

Draw in the image of the object. The head of the image is located where either solid lines or dotted lines converge. The bottom of the image is located on the principle axis.

Convex Mirror

f =

do =

ho =

f CFor each drawing, complete each of the following:

Measure the image distance (di)Measure the image height (hi)Bigger or Smaller?Erect or Inverted?Real or Virtual?

di = - 3.4 cm

hi = 1.5 cm

Smaller

Erect

Virtual

Convex Mirror

f =

do =

ho =

Mathematical Method for Locating the Image

Magnification

Practice!!

Given the following information, use ray diagrams to locate the image. Then calculate the image location and size using the mathematical method.

Type of Mirror Focal Length Object Distance Object Height

Convex -7.0 cm 3.0 cm 5.0 cm

Convex -3.0 cm 8.0 cm 2.0 cm

Concave 5.0 cm 12.0 cm 2.0 cm

Concave 6.5 cm 2.0 cm 3.5 cm

Important Reminders

Use only one sheet of plain white paper for each drawing

You must use at least two colors on each drawing- but it might be best to use light pencil first and trace over the lines later.

The dotted lines are always an extension of the reflected ray, not the ray that is incident on the mirror.

Thin lenses are not “spherical” in shape.

Our drawings use lenses that have two curved surfaces

Therefore there is no Center of Curvature

With two curved surfaces,

In a sense you have two focal points, on each side of the lens.

As long as each has the same amount of curve, the focal length will be equal on both sides.

f f

The biggest and most important difference:

The solid lines on your drawings will be the ones passing through the lens to the right side of your drawing.

Refraction, not reflection is occurring.

Converging Lens Diverging Lens

f f

Ray 1Ray 2

Ray 3

di =

hi =

Smaller

Inverted

Real

Each drawing will require five (5) quick calculations based on the given information and your measurements.

These are the calculations you will make:

Image distance

Magnification using image height and object height

Magnification using image distance and object distance

Percent Error : Measured image distance vs. calculated image distance

Percent Error : Magnification (using measured hi and given ho) vs. Magnification (calculated di and measured do)

Equations:

The same equations work for spherical mirrors and symmetrical thin lenses.

io ddf

111

This equation relates focal length, object distance, and image distance.

Use this equation to calculate di.

Equations:

Magnification can be calculated two ways:

Compare hi to ho

Compare di to do

o

i

h

hM

o

i

d

dM

Based on a measurement of image

height

Based on a calculated image distance

Just how well did you draw the ray diagrams?

Percent ErrorPercent Error : Measured image distance vs. calculated image distance

Percent Error : Magnification (using measured hi and given ho) vs. Magnification (calculated di and measured do)

100) (

) () (

i

ii

dcalculatedActual

dmeasuredObserveddcalculatedActual

100)d and d CALCULATED using Mag(

)h and h using Mag()d and d CALCULATED using Mag(

oi

oioi

Actual

ObservedActual

Ray diagram Equations

1. Calculate di using:

2. Calculate Magnification using:

3. Calculate Magnification using:

4. Calculate Percent Error

5. Calculate Percent Error

io ddf

111

o

i

h

hM

o

i

d

dM

Calculated!

100) (

) () (

i

ii

dcalculatedActual

dmeasuredObserveddcalculatedActual

100)d and d CALCULATED using Mag(

)h and h using Mag()d and d CALCULATED using Mag(

oi

oioi

Actual

ObservedActual

f f

di = +7.50 cmhi = -1.10 cmSmallerInvertedReal

f = +4.5 cm

do = 10.9 cm

ho = 1.5 cm

Calculations: (On Back of your Drawings)

1 cmdidd ii

69.71

092.222.1

9.10

1

5.4

1

2 73.5.1

10.1

cm

cmM

3 71.90.10

69.7

cm

cmM

4 %5.210069.7

50.769.7

5 %8.210071.

73.71.

Drawing # Type of Mirror/Lens Focal length, Object distance, Object Height

1 Convex Mirror

f = -7.0 cmdo = 3.0 cm

ho = 5.0 cm

2 Convex Mirror

f = -3.0 cmdo = 8.0 cm

ho = 2.0 cm

3 Convex Mirror

f = -6.0 cmdo = 6.0 cm

ho = 2.5 cm

4 Concave Mirror

f = 5.0 cmdo = 12.0 cm

ho = 2.0 cm

5 Concave Mirror

f = 6.5 cmdo = 2.0 cm

ho = 3.5 cm

6 Concave Mirror

f = 4.0 cmdo = 4.0 cm

ho = 2.0 cm

7 Converging Lens

f = 10.0 cmdo = 4.0 cm

ho = 2.0 cm

8 Converging Lens

f = 7.5 cmdo = 7.5 cm

ho = 3.0 cm

9 Converging Lens

f = 6.0 cmdo = 11.0 cm

ho = 4.5 cm

10 Converging Lens

f = 6.0 cmdo = 12.0 cm

ho = 3.0 cm

11 Diverging Lens

f = -5.0 cmdo = 8.0 cm

ho = 3.5 cm

12 Diverging Lens

f = -10.0 cmdo = 5.0 cm

ho = 3.0 cm

Example Exercise

When an object is placed 75 cm away from a concave mirror, an image is produced that is real and twice the size of the object. What must be the focal length of the mirror?

Equations for Mirrors and Lenses

only) mirrors(for 2 fC

io ddf

111

o

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o

i

d

dM

h

hM

When an object is placed 75 cm away from a concave mirror, an image is produced that is real and twice the size of the object. What must be the focal length of the mirror?

Lens Activity

Which lenses will allow a real image to be formed

How does the side that light is incident upon change the focal length?

Lens Makers Equations

21

111

1

RRn

n

f env

lens

Important Rules for the side light is incident upon:

•R is positive when C is on the side of the lens that light emerges

•R is negative when C is on the side of the lens on which light is incident

Lens Makers Equations

21

111

1

RRn

f lens

As long as there is air surrounding the lens, then nenv= 1, so the equation looks like this:

If the focal length is measured in meters, then 1/f has a unit of diopters (D), and this represents the power of the lens

Lens Makers Equations

21

111

1

RRn

f lens

As long as there is air surrounding the lens, then nenv= 1, so the equation looks like this:

The radius of curvature for the curved surface that light is incident upon

The radius of curvature for the surface that light is exiting through

Using the Lens Makers Equation

An optometrist prescribes a corrective lens with a power of +1.5 diopters. The lens maker will start with a glass blank that has an index of refraction of 1.6 and a convex front surface whose radius of curvature is 20cm. To what radius of curvature should the other surface be ground?

Quiz topics

21

111

1

RRn

f lens

only) mirrors(for 2 fC

io ddf

111

o

i

o

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d

dM

h

hM

Human VisionNearsighted vs. FarsightedLensRetina

Mirrors and Lenses

Lens Makers’ Equations