Properties of Waves 2

PSC 20

Plane Mirror/Law of Reflection Activity

Law of Reflection• the angle of incidence is always equal to

the angle of reflection.

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Laws of Reflection• mirrors are opaque surfaces which reflect

light.Incident Rays - The ray approaching the mirror.Reflected Ray - the ray reflected by the mirror.Point of Incidence - where the incident ray

meets the mirror.Normal - Perpendicular to the mirror from the

point of incidence.Angle of Incidence - the angle between the

incident ray and the normal.Angle of Reflection - the angle between the

reflected ray and the normal.• The angle of incidence is always equal to the

angle of reflection.

MIRROR

NORM

AL

θi θr

Incident Ray Reflected Ray

Point of incidence

http://www.physicsclassr http://www.physicsclassroom.com/mmedia/op

tics/lr.gif oom.com/mmedia/optics/lr.gif

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Specular (regular) vs Diffuse reflectionWhy do some reflection look like mirrors and other don’t?

microscopically smooth surfaces reflect light in a predictable way, while microscopically rough surfaces scatter it.

Plane Mirror/Law of Reflection Activity

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•when you see an image in a mirror, your eye cannot tell that light has been reflected.

• the light appears as though it is behind the mirror (this is referred to as a virtual image).

•when you look at yourself in the mirror and raise your right hand, the image appears to raise its left hand. This is called lateral inversion.

PLANE MIRROR

MIRROR

x x=

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Characteristics of Images in a Plane MirrorSame size as objectVertically erectVirtualLaterally invertedThe image is the same distance behind the mirror as the object is in front of the mirror.

L = behind the mirror, same distance as objectO = erectS = same sizeT = virtual

• Why do Plane Mirrors Flip Horizontally and not Vertically?

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Curved MirrorsThere are two types:

1) Concave mirror (converging mirror) - makes parallel light rays converge together.

2) Convex mirror (diverging mirror) - makes parallel light rays diverge apart.

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Diverging Mirror

Converging Mirror

Concave (Converging) Spherical MirrorsConverging

FParallel light rays are reflected through a 

Focal Point (F)

Parts of a Ray DiagramMirror

Principal Axis (P.A.)

C

C = Centre of Curvature

Vertex(V)

F

F = Focal Point (half way between C & V)

r

r = Radius of Curvaturef = Focal Distance

f

(f =1/2r)

Draw two rays starting from the tip of the arrow and reflect them off the mirror. 

The image forms where the two rays cross after reflecting off the mirror.

Drawing a Ray Diagram

1.Rays parallel to the P.A. reflect through F.

2.Rays through F reflect parallel to the P.A.

3.Rays through C reflect back through C.

Ray Rules

CF

Object Beyond the Centre of Curvature

LOSTL‐In Front between F & C O‐InvertedS‐SmallerT‐Real

C F

Object Inside the Focal Point

LOSTL‐Behind MirrorO‐ErrectS‐LargerT‐Virtual

`

Examples

1) f = 4.0 cm do = 8.0 cm ho = 1.0 cm

2) f = 4.0 cm do = 4.0 cm ho = 1.0 cm

3) f = 4.0 cm do = 2.0 cm ho = 1.0 cm

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Rules For Rays in a Diverging Mirror1. A ray that is parallel to the principle axis is

reflected from the principle focus.2. A ray that travels towards the principle focus is

reflected parallel to the principle axis.3. A ray that travels towards the center of curvature

is reflected back along the same path.

C

Practice

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Rules For Rays in a Diverging MirrorDiverging mirrors always produce an image:L – behind the mirror (between vertex and f)O - erectS - smallerT - virtual

C

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Images formed by Diverging Mirrors• The principle focus (F) and the center of

curvature (C) are virtual, behind the mirror• Diverging mirrors only create virtual

images that are erect, smaller than the original object, and located between the vertex and the principle focus.

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Equations for Curved Mirrors

The curved mirror equation is given as:1 = 1 + 1f do di

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Sign Conventions1) All distances are measured from the vertex.2) Distances of real images and f are positive.3) Distances of virtual images and f are negative.4) When measured upwards, hi and ho are

positive. They are negative when measured downwards.

5) di and hi can never have the same sign

The Magnification Equation is: M = hi = -diho do

The magnification is positive for an erect image and negative for an inverted image.

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Sample Problems1) An object is located 30.0 cm from a converging

mirror with a focal length of 5.0 cm. (a) At what distance from the mirror will the image be formed? (b) If the object is 4.0 cm tall, how tall is the image?

do = 30.0 cmdi = ?f = 5.0 cm

1 = 1 +  1f do di1 =  1 + 15.0 30.0 di0.2 = 0.03… + 1/di0.16… = 1/didi = 6.0 cm

do = 30.0 cmdi = 6.0 cmf = 5.0 cmho = 4.0 cmhi = ?

M =  hi =  ‐diho dohi =  ‐6.0 cross multiply4.0 30.0hi = ‐0.80 cm

You can also re‐arrange for hi 

M =  hi  =  ‐diho  dohi  =  (‐di)(ho)

  dohi  =  (‐6.0)(4.0)

  30.0hi = ‐0.80 cm

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2) A diverging mirror with a focal length of 5.0 cm produces an image 4.0 cm from the mirror. (a) What is the distance of the object from the mirror? (b) What is the magnification?

Curved Mirror Drawing and Calculation Assignment

Text Questions

do = ?di = ‐4.0 cm* (virtual images have –di)f = ‐5.0 cm* (virtual f is –) 

1 = 1  +   1f do di1   =    1     +   1   ‐5.0 do ‐4.0‐0.2 = 1/do  ̶   0.250.05 = 1/dodo = 20.0 cm

do = ?di = ‐4.0 cm*f = ‐5.0 cm*do = 20.0 cm

M =  hi =  ‐diho do

M =  ‐(‐4.0)20.0

M = +0.20

Spherical vs Parabolic Mirrors

Reflection with a Parabolic Surface

All the waves are reflected to a single point (referred to as the focal point).

PSC20

Curved Mirror Lab

ImageCharacteristics

Summary

- virtual distancesare negative

Mirror Equation Magnification Equation

- negative values mean the image is inverted.

Concave mirrors have a positive focal length,convex mirrors have a negative focal length.