Curved MirrorsCurved Mirrors

Two types of curved Two types of curved mirrorsmirrors

1.1. Concave mirrorsConcave mirrors – inwardly – inwardly curved inner surface that curved inner surface that converges incoming light rays. converges incoming light rays.

2.2. Convex MirrorsConvex Mirrors – outwardly – outwardly curved, mirrored surface that curved, mirrored surface that diverges incoming light rays. diverges incoming light rays.

Concave mirrors…Concave mirrors…

can form BOTH can form BOTH virtualvirtual and and realreal images of an object depending images of an object depending on how far the object is placed on how far the object is placed away from the mirror.away from the mirror.

Real image: Real image: an image formed an image formed when light rays intersect at a when light rays intersect at a single point.single point.

Image location can be predicted Image location can be predicted with mirror equations.with mirror equations.

Concave mirrorsConcave mirrors

Principal axis

Center of Curvature ( C )

Focal Length ( f )

Object distance ( p )

h

1/object distance + 1/image distance = 1/object distance + 1/image distance = 1/focal length1/focal length

1/p + 1/q = 1/1/p + 1/q = 1/ff

Images produced by concave mirrors Images produced by concave mirrors (virtual or real) will NOT be the (virtual or real) will NOT be the same size of our object.same size of our object.

They will be magnified (M)They will be magnified (M)

magnification = magnification = image heightimage height = - = - image image distancedistance

object height object object height object distancedistance

M = h'/h = - q/pM = h'/h = - q/p

+ M = upright and virtual image+ M = upright and virtual image- M = inverted and real image- M = inverted and real image

Concave mirrorsConcave mirrors

Rules for drawing Rules for drawing reference linesreference lines

Ray Line from object Line from mirror to Ray Line from object Line from mirror to

to mirror to mirror reflected imagereflected image

1. Parallel to principal Through focal point 1. Parallel to principal Through focal point axis Faxis F

2. Through focal point parallel to principal 2. Through focal point parallel to principal

F axisF axis

3. Through the center back along itself 3. Through the center back along itself through through

of curvature C Cof curvature C C

Object distance is greater Object distance is greater than the focal lengththan the focal length

Principal axis

Reflecting Surface

Ray DiagramRay Diagram

fC

Object distance is less than Object distance is less than the focal lengththe focal length

Principal axis

Reflecting Surface

Ray DiagramRay Diagram

fC

Convex MirrorsConvex Mirrors

Focal point and center of Focal point and center of curvature are located behind the curvature are located behind the mirror’s surface.mirror’s surface.

Magnification (M) is always +, Magnification (M) is always +, but it is less than 1but it is less than 1

Image is always virtualImage is always virtual

Provide a large field of viewProvide a large field of view

Convex MirrorsConvex Mirrors

Principal axis

f C

Reflecting Surface

Lens Characteristics Lenses are objects that refract light rays.

Converging Lens Diverging Lens

Two refracting surfaces Rays will either converge or diverge to

create an image. Two Types:

Lens Characteristics

f f

ff

Converging Lenses Produce either real or virtual images

Object distance > f = real image, opposite side

Object placed closer than f = virtual image, same side

Object placed at infinity = point image on opposite f

(ex. Sun & magnifying glass) pg. 571 Fig. 15.3

Object at f = image at infinity (ex. Lighthouses) Fig. 15.3

Ray Diagram (Converging Lens)

f fP-Axis

1

1. In parallel to P-axis, out to f point

2. To center of lens, out center of lens3. Passes through f, out parallel to P-axis

23

Image

THE HUMAN EYE

P-Axis f f

1

2

3

Image

Ray Diagram (Converging Lens)

Binoculars, microscopes, & telescopes

Diverging Lenses

Only produces virtual images on the same side as the object.

Object distance > f = image is larger

Object distance < f = image is smaller

Used to correct nearsightedness

Ray Diagram (Diverging Lens)

ff

1. In parallel to P-axis, out away from f point2. To center of lens, out center of lens3. Travels towards opposite f, out parallel to P-axis

Image

1

2

3

Thin Lens Equation

Is identical to the mirror equation and can be used for both convergent and divergent lenses.

1 + 1 = 1

do di f

+ do = object in front of lens - do = object behind lens

+ di = image behind lens - di = image in front of lens

+ f = converging lens - f = diverging lens

Magnification of a Lens

Formula is also identical to mirror magnification formula:

M = hi = - di

ho do

+ M = virtual, upright image

- M = real, inverted image