PROOF OF dPROOF OF dii = d = doo

i

r

12

DESCRIPTION OF dDESCRIPTION OF dii = d = doo

Ray of light leaves base & strikes mirror at Ray of light leaves base & strikes mirror at ii (reflected at same (reflected at same ))

Angles Angles 11 and and 22

+ + 11 = 90 = 90oo

+ + 22 = 90 = 90oo

But But is equal to is equal to rr Opposite angles formed by intersecting linesOpposite angles formed by intersecting lines Therefore Therefore 11 = = 22

MIRRORS AT RIGHT ANGLESMIRRORS AT RIGHT ANGLES

IMAGE 1

IMAGE 3

IMAGE 2

RIGHT ANGLES CONTINUEDRIGHT ANGLES CONTINUED

What would be the equation for the number of What would be the equation for the number of images formed when the angle between two mirrors images formed when the angle between two mirrors is is

(360o/) - 1(360o/90o) - 1 = 3images formed(360o/60o) - 1 = 5images formed

FOCAL LENGTH OF CONCAVE FOCAL LENGTH OF CONCAVE MIRRORMIRROR

Incident ray strikes at AIncident ray strikes at A

Line CA is radius of mirror (normal Line CA is radius of mirror (normal to surface)to surface)

Reflected ray is reflected at angle Reflected ray is reflected at angle equal to incidentequal to incident

Angle ACF is also Angle ACF is also – CA is – CA is transversal of two parallel linestransversal of two parallel lines

ACF is isosceles – CF & FA are ACF is isosceles – CF & FA are equal equal

When incident ray is close to PA, q is When incident ray is close to PA, q is small small

Therefore CF = FA = FBTherefore CF = FA = FB

Focal length is ½ of radiusFocal length is ½ of radius

RAY DIAGRAMS FOR CURVED RAY DIAGRAMS FOR CURVED MIRRORSMIRRORS

CONCAVE MIRRORSCONCAVE MIRRORS Inside surface is Inside surface is

polishedpolished

Law of reflection Law of reflection applies for curved applies for curved mirrors as well (mirrors as well (ii = = rr))

Converging Mirror – Converging Mirror – Light is concentrated Light is concentrated at one pointat one point

CONCAVE MIRRORSCONCAVE MIRRORS

Center of curvature – center of curved mirror Center of curvature – center of curved mirror (similar to center of circle)(similar to center of circle)

Principle axis – Straight line drawn through C & the Principle axis – Straight line drawn through C & the center of mirror.center of mirror.

Focal point – Point where all light will focus (half Focal point – Point where all light will focus (half the distance of C)the distance of C)

DRAWING RAYSDRAWING RAYSNeed to draw 3 raysNeed to draw 3 rays

All rays start from the top (head) of the objectAll rays start from the top (head) of the object

11stst ray – Incoming ray is parallel to the ray – Incoming ray is parallel to the principle axis & is reflected through the focal principle axis & is reflected through the focal point.point.

22ndnd ray – Incoming ray goes through the focal ray – Incoming ray goes through the focal point & is reflected parallel to the principle point & is reflected parallel to the principle axisaxis

33rdrd ray – Serves as a check ray – Serves as a check Incoming ray goes through the center of curvature Incoming ray goes through the center of curvature

& is reflected back along the same line.& is reflected back along the same line.

IMAGE FORMATIONIMAGE FORMATION

The image is formed where the three The image is formed where the three reflected rays cross.reflected rays cross.

Drawn from the principle axis to the Drawn from the principle axis to the point of intersectionpoint of intersection

If the three rays cross on the same side If the three rays cross on the same side of the mirror as the object, the image is of the mirror as the object, the image is considered a real imageconsidered a real image

If the three rays cross on the opposite If the three rays cross on the opposite side of the mirror, the image is consider side of the mirror, the image is consider virtualvirtual

SIGN CONVENTION FOR SIGN CONVENTION FOR SPHERICAL MIRRORSSPHERICAL MIRRORS

FOCAL LENGTH OBJECT DISTANCE

IMAGE DISTANCE

MAGNIFICATION

f + for concave mirror

do is + if object in front of mirror

di is + if image is in front of mirror

m is + when image is upright

f is – for convex mirror

do is – if object behind mirror

di is – if image is behind mirrror

m is – when image is inverted

*IF IMAGE IS IN FRONT OF MIRROR (SAME SIDE AS OBJECT), IT IS CONSIDERED A REAL OBJECT

**IF IMAGE IS BEHIND MIRROR (OPPOSITE SIDE AS OBJECT), IT IS CONSIDERED A VIRTUAL OBJECT

CONVEX MIRRORCONVEX MIRROR Outside surface is polishedOutside surface is polished

Law of reflection applies as wellLaw of reflection applies as well

Diverging mirror – reflected rays will never Diverging mirror – reflected rays will never cross in front of mirror (same side as object)cross in front of mirror (same side as object)

CONVEX MIRRORCONVEX MIRROR Center of curvature is Center of curvature is

still the same but is still the same but is considered a considered a negative value since negative value since it is on the back side it is on the back side of the mirrorof the mirror

Focal point is also Focal point is also considered a considered a negative value for negative value for the same reason (half the same reason (half the distance of C)the distance of C)

IMAGES FORMED FROM IMAGES FORMED FROM CONVEX MIRRORCONVEX MIRROR

Still draw the same 3 rays to locate the Still draw the same 3 rays to locate the imageimage

Since the reflected rays will never cross on Since the reflected rays will never cross on the same side as the object, these rays must the same side as the object, these rays must be drawn (as dotted lines) behind the mirrorbe drawn (as dotted lines) behind the mirror

Where they cross is where image is locatedWhere they cross is where image is located

Image is considered a virtual imageImage is considered a virtual image

Virtual image – Light rays do not pass Virtual image – Light rays do not pass through the imagethrough the image

HOMEWORKHOMEWORK

Draw the following diagrams:Draw the following diagrams: Object beyond CObject beyond C Object @ CObject @ C Object between C and fObject between C and f Object at fObject at f Object between f and surface of mirrorObject between f and surface of mirror

11stst four diagrams: C = 10 cm, h four diagrams: C = 10 cm, hoo = 2 cm concave = 2 cm concave mirrormirror

55thth diagram C = 6 cm h diagram C = 6 cm hoo = 1 cm convex mirror = 1 cm convex mirror

CONCAVE MIRRORCONCAVE MIRROR

MIRROR AND MIRROR AND MAGNIFICATION EQ.MAGNIFICATION EQ.

f = focal length of mirrorf = focal length of mirror

do = object distancedo = object distance

di = image distancedi = image distance

m = magnification of the mirror – ratio of height of m = magnification of the mirror – ratio of height of image to height of objectimage to height of object