Curved MirrorsCurved Mirrors

Chapter 13 Section 3Chapter 13 Section 3

Mirror TerminologyMirror Terminology

CC center of curvaturecenter of curvature RR radius of curvatureradius of curvature

Mirror TerminologyMirror Terminology

Virtual image – Virtual image – produced at a produced at a point where light point where light rays appear to rays appear to come fromcome from

Real image – Real image – produced when produced when rays of light rays of light intersect (can intersect (can be displayed on be displayed on a surface)a surface)

Mirror TerminologyMirror Terminology

pp object distanceobject distance qq image distanceimage distance

Mirror TerminologyMirror Terminology

hh object heightobject height h’h’ image heightimage height

Mirror TerminologyMirror Terminology

InvertedInverted UprightUpright

Mirror TerminologyMirror Terminology

FF focal pointfocal point ff focal length (also equal to ½ focal length (also equal to ½ RR))

Concave MirrorsConcave Mirrors

Curved inwardCurved inward Converges light raysConverges light rays Used to produce magnified virtual imagesUsed to produce magnified virtual images Can also produce real imagesCan also produce real images Example use = make-up mirrorExample use = make-up mirror

Convex MirrorsConvex Mirrors

Outwardly curvedOutwardly curved Diverges light raysDiverges light rays Image is always virtualImage is always virtual Image distance is always negativeImage distance is always negative Focal length is always negativeFocal length is always negative

Uses of Convex MirrorsUses of Convex Mirrors

Can provide a view of a Can provide a view of a large area (like in a large area (like in a convenience store)convenience store)

Used on passenger Used on passenger side-view mirrors with side-view mirrors with the warning “objects the warning “objects are closer than they are closer than they appear”appear”

Ray diagrams for curved Ray diagrams for curved mirrorsmirrors

1. Tip of object to mirror parallel to 1. Tip of object to mirror parallel to principal axis (reflects through focal principal axis (reflects through focal point)point)

2. Tip of object on a line that contains the 2. Tip of object on a line that contains the focal point (reflects parallel to principal focal point (reflects parallel to principal axis)axis)

3. Tip of object through center of 3. Tip of object through center of curvature (reflects back along itself)curvature (reflects back along itself)

Mirror ConventionsMirror Conventions

In front (of a mirror) = leftIn front (of a mirror) = left Displacements to the left of a mirror are + Displacements to the left of a mirror are + Displacements to the right of the mirror are –Displacements to the right of the mirror are – Example: q is +when the image is real but -when Example: q is +when the image is real but -when

the image is virtualthe image is virtual Displacements above the principal axis are +Displacements above the principal axis are + Displacements below the principal axis are –Displacements below the principal axis are – Example: h’ is + when the image is upright and – Example: h’ is + when the image is upright and –

when the image is invertedwhen the image is inverted

Mirror EquationMirror Equation

Can be used to predict image locationCan be used to predict image location

1/p + 1/q = 1/f1/p + 1/q = 1/f

Magnification EquationMagnification Equation

Relates image size to object sizeRelates image size to object size MM<1 = image smaller than object<1 = image smaller than object M>1 = image larger than objectM>1 = image larger than object M is - when image is invertedM is - when image is inverted M is + when image is uprightM is + when image is upright

M = h’ = - qM = h’ = - q

hh p p

#1 The surface of a concave #1 The surface of a concave mirror is pointed towards the mirror is pointed towards the sun. Light from the sun hits the sun. Light from the sun hits the mirror and converges to a mirror and converges to a point. How far is this point. How far is this converging pointconverging point from the from the mirror's surface if the radius of mirror's surface if the radius of curvature (R) of the mirror is curvature (R) of the mirror is 150 cm?150 cm?

#1 Answer#1 Answer

Hint: What is the relationship between Hint: What is the relationship between the center of curvature and the focal the center of curvature and the focal point of a mirror?point of a mirror?

R = 2fR = 2f Because R = 150, f = 75 cm Because R = 150, f = 75 cm

#2 If p=7cm and q=3cm, #2 If p=7cm and q=3cm, find f.find f.

#2 Answer#2 Answer

f = 2.1 cmf = 2.1 cm The positive value for f tells us that this is The positive value for f tells us that this is

a concave mirror.a concave mirror.

#3 If the object is 5cm from #3 If the object is 5cm from a mirror whose focal point a mirror whose focal point is 10 cm, what will the is 10 cm, what will the image distance be?image distance be?

#3 Answer#3 Answer

q = -10 cm q = -10 cm The negative sign tells us that the image The negative sign tells us that the image

is…is… virtualvirtual

#4 Calculate the image #4 Calculate the image height of an 8 cm object height of an 8 cm object when p = 12 cm and q = when p = 12 cm and q = 3 cm.3 cm.

#4 Answer#4 Answer

h‘ = - 2 cmh‘ = - 2 cm Because h’ is less than h, the image is…Because h’ is less than h, the image is… reducedreduced Because the h’ value is negative, the Because the h’ value is negative, the

image is… image is… invertedinverted

#5 The image formed by #5 The image formed by a concave mirror is a concave mirror is upright and virtual. upright and virtual. What would be the signs What would be the signs for R, f, q, and h’?for R, f, q, and h’?

#5 Answer#5 Answer

What would be the signs for R, f, q, and What would be the signs for R, f, q, and h’? h’?

R is + because this is a concave mirrorR is + because this is a concave mirror f is + because this is a concave mirrorf is + because this is a concave mirror q is – because the image is virtualq is – because the image is virtual h‘ is + because the image is uprighth‘ is + because the image is upright