Image of a point dodo didi A’A’ A Due to the similarity of the triangles on the diagram, all the reflected rays extend backward to one point. No matter where the observer is, the image is always: Behind the mirror On the perpendicular line drawn from the object, A. At the same distance from the mirror as object.

Image Formation in Plane Mirrors by a Point Source of Light dodo didi A 1 A’A’ To construct the image of a point, -sketch a line perpendicular to the mirror through A - measure d o (from A to the mirror surface) - construct image A' on the other side such as d o = d i Because all the reflected light rays intersect at one point anyway, there is no need to construct many of them, but only one: the perpendicular to the surface of the mirror.

Image Formation in Plane Mirrors To construct the image of an object, there is no need to construct an image of each single point of it. Construct an image of the extreme points (e.g. top and the bottom), then connect these edge points

Properties of Images Formed by Plane Mirrors S A L T ttitude ize ocation ype The image has the same size as the object (no magnification) The image is up-right but Laterally Inverted (Left / Right) Image is at the same distance from mirror as the object (see the next slide first)

Type of the images formed by plane mirrors Our eye catches diverging rays reflected from mirror. Observer has a sensation that image is at the intersection of the light rays extended behind the mirror. There is nothing behind the mirror. Light only appears to us to come from this point.This image is imaginary, or virtual image because there is no real light rays going to or coming from behind the mirror.

Properties of Images Formed by Plane Mirrors S A L T ttitude ize ocation ype The image has the same size as the object (no magnification) The image is up-right but Laterally Inverted (Left / Right) Image is at the same distance from mirror as the object Plane mirrors form virtual images

7 Spherical Mirrors A spherical mirror has the shape of a section of a sphere.

8 Concave Concave Mirrors have the reflecting surface inside of the curve AKA Converging mirrors as parallel to the axis rays are reflected inward

9 Concave Mirror Terminology Principal axis: line connecting the centre of curvature with the mirror’s vertex Is the centre of the sphere the mirror is cut from. The length of C is the radius of the sphere Focal Point (focus) : where all parallel to the axis incident rays meet after reflection in the mirror. Vertex: centre of the mirror, located on axis Concave Mirror: a mirror with reflecting surface curved inward Focal distance from F to V

10 Four Principal rays of Concave Mirrors

11 Image Formation using Ray Diagrams for a Concave Mirror: Principal Rays Summary Incident RayReflected Ray Parallel to principal AxisThrough the focal point Parallel to principal Axis Through C On the vertex of the mirrorSuch as angle with axis is same for incident and reflected ray

Images formed by Concave Mirrors Watch video showing image formed by a curved mirrorvideo 12

How do we see the image A point object emit (or reflect) light in all directions 13 All the rays reflected by mirror meet at one point Eye detects light coming out of that point Brain identifies this point as the image

Ray Diagrams for a Non-Point Source 14 For non-point objects, construct images of few extreme point. O O’O’ For perpendicular to the axis objects, locate the image of the top, Connect with axis at right angle to locate the bottom of the image Any point on axis will form image on axis.

Practice Practice constructing ray diagrams for 5 different locations of the object Note that the properties of these images will be quite different. 15

16 Object is Located beyond the Centre of Curvature S: smaller A: inverted L: between F and C T: real

17 Object is located at the Centre of Curvature Think of mirror as almost flat close to axis to avoid spherical aberration Image Properties: S: same as obect A: Inverted L: at C T: real This image is very convenient in determining the mirror’s focal length

18 Object Located between F and C S: bigger A: inverted L: beyond C T: real

19 Object is located at Focal Point S: N/A A: N/A L: N/A T: N/A Light rays are parallel, they never meet. No image formed: no properties

20 Object in between Focal point and Mirror Size: Enlarged Attitude: Up-right Location: Behind the mirror Type: Virtual F C This time, converging mirror actually converges the light rays. Demo reminder: large mirror

21 Concave Mirror Image Properties Summary Object location SizeAttitudeLocationType d o > csmallerinvertedf < d i < cReal d o = csameinvertedd i = cReal f < d o < cbiggerinvertedd i > cReal d o = fN/A d o < fbiggerup-rightAnywhere behind the mirror Virtual

22 Sample Problem – Scale Ray Diagram A pencil 15 cm high is located 60 cm in front of a concave mirror with a focal length of 20 cm. Construct a scale diagram to correctly determine the location of the image and its height. (indicate the scale used)