AP Physics B Mrs. Wallace

Reflection Reflection occurs when light bounces off a surface. There are two types of reflection Specular reflection Off a shiny surface Diffuse reflection Off a rough surface

Mirrors are great reflectors Plane Mirror shiny + dark - shiny + + dark - - Spherical Mirrors convex concave

Light Rays Mathematical rays never bend But light rays can, if they interact with materials!

Let’s take a closer look at a plane mirror Plane Mirror +- Incident ray Reflected ray normal A normal is a line that is perpendicular to the mirror.

Ray tracing Ray tracing is a method of constructing an image using the model of light as a ray. We use ray tracing to construct optical images produced by mirrors and lenses. Ray tracing lets us describe what happens to the light as it interacts with a medium.

Law of Reflection The angle of incidence of reflected light equals the angle of reflection.  r =  I Note that angles are measured relative to a normal to the mirror surface. shiny (+)dark (-) plane mirrorlight source incident ray normal reflected ray rr ii

Optical images Nature real (converging rays) virtual (diverging rays) Orientation upright inverted Size true enlarged reduced

Ray tracing: plane mirror Construct the image using two rays. +- object 5 cm Image -5 cm Reflected rays are diverging. Extend reflected rays behind mirror. Name the image: Virtual, upright, true size

Spherical mirrors There are two types of spherical mirrors shiny concaveconvex (where reflected rays go) (dark side) Focal length, f, is positive Focal length, f, is negative

Parts of a Spherical Concave Mirror Principle axis + - These are the main parts of a spherical concave mirror. The focal length is half of the radius of curvature. The focal length is positive for this type of mirror. R = 2f Focus f Center R

Identification of the focus of a spherical concave mirror + - Rays parallel to the principle axis all pass through the focus for a spherical concave mirror.

Ray tracing: spherical concave mirror The three “principle rays” to construct an image for a spherical concave mirror are the p-ray, which travels parallel to the principle axis, then reflects through focus. the f-ray, which travels through focus, then reflects back parallel to the principle axis. the c-ray, which travels through center, then reflects back through center. You must draw two of the three principle rays to construct an image.

Ray tracing: spherical concave mirror Construct the image for an object located outside the center of curvature. It is only necessary to draw 2 of the three principle rays! CF Real, Inverted, Reduced Image p f c

C F Real, Inverted, True Image Ray tracing: spherical concave mirror Construct the image for an object located at the center of curvature. Name the image.

CF Real, Inverted, Enlarged Image Ray tracing: spherical concave mirror Construct the image for an object located between the center of curvature and the focus. Name the image.

C F No image is formed. Construct the image for an object located at the focus. Ray tracing: spherical concave mirror

CF Virtual, Upright, Enlarged Image Construct the image for an object located inside the focus. Name the image. Ray tracing: spherical concave mirror

Problem a) Construct 2 ray diagrams to illustrate what happens to the size of the image as an object is brought nearer to a spherical concave mirror when the object outside the focus. b) Repeat part a) for an object which is brought nearer to the mirror but is inside the focus.

Solution a) The image becomes larger when you move the object closer.

Solution b) The image becomes smaller when you move the object closer.

Mirror equation #1 1/s i + 1/s o = 1/f s i : image distance s o : object distance f: focal length

Mirror equation # 2 M = h i /h o = -s i /s o s i : image distance s o : object distancem h i : image height h o : object height M: magnification

Sample Problem A spherical concave mirror, focal length 20 cm, has a 5- cm high object placed 30 cm from it. a)Draw a ray diagram and construct the image. c)Name the image

Sample Problem A spherical concave mirror, focal length 20 cm, has a 5- cm high object placed 30 cm from it. b)Use the mirror equations to calculate i.the position of image ii.the magnification iii.the size of image

Parts of a Spherical Convex Mirror These are the main parts of a spherical convex mirror. The focal length is half of the radius of curvature, and both are on the dark side of the mirror. The focal length is negative for this type of mirror. Principle axis CenterFocus + -

Ray tracing: spherical convex mirror Construct the image for an object located outside a spherical convex mirror. Name the image. FC Virtual, Upright, Reduced Image

Problem A spherical concave mirror, focal length 10 cm, has a 2- cm high object placed 5 cm from it. a)Draw a ray diagram and construct the image.

Problem A spherical concave mirror, focal length 10 cm, has a 2- cm high object placed 5 cm from it. b)Use the mirror equations to calculate i.the position of image ii.the magnification iii.the size of image c)Name the image

Problem A spherical convex mirror, focal length 15 cm, has a 4-cm high object placed 10 cm from it. b)Use the mirror equations to calculate i.the position of image ii.the magnification iii.the size of image c)Name the image

Summary Concave vs convex mirrors Concave Image is real when object is outside focus Image is virtual when object is inside focus Focal length f is positive Convex Image is always virtual Focal length f is negative