Chapter 13 Light and Reflection Ms. Hanan Anabusi

13-3 Curved Mirrors Objectives: Calculate distances and focal lengths using mirror equation for concave and convex spherical mirrors. Draw ray diagrams to find the image distance and magnification for concave and convex spherical mirrors. Distinguish between real and virtual images. Describe how parabolic mirrors differ from spherical mirrors.

Vocabulary Spherical mirror Concave Convex Parabolic Focal point Focal length Center of curvature Radius Principal axis

Spherical Mirrors (concave & convex)

Concave & Convex (just a part of a sphere) • F • f C: the center point of the sphere (center of curvature) R: radius of curvature (just the radius of the sphere) F: the focal point of the mirror or lens (halfway between C and the sphere) f: the focal distance, f = R/2

Concave Mirrors (curved in) principal axis C • F • Light rays that come in parallel to the principal axis reflect through the focal point.

Concave Mirror (example) principal axis C • F •

Concave Mirror (example) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point.

Concave Mirror (example) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

Concave Mirror (example) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A real image forms where the light rays converge.

Concave Mirror (example 2) principal axis C • F •

Concave Mirror (example 2) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point.

Concave Mirror (example 2) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

Concave Mirror (example 2) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. The image forms where the rays converge. But they don’t seem to converge.

Concave Mirror (example 2) principal axis C • F • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. A virtual image forms where the sight rays converge.

Your Turn (Concave Mirror) principal axis object C • F • concave mirror Note: mirrors are thin enough that you just draw a line to represent the mirror Locate the image of the arrow

Your Turn (Concave Mirror) principal axis object C • F • concave mirror Note: the mirrors and lenses we use are thin enough that you can just draw a line to represent the mirror or lens Locate the image of the arrow

Convex Mirrors (curved out) principal axis F • Light rays that come in parallel to the principal axis reflect from the focal point. The focal point is considered virtual since sight lines, not light rays, go through it.

Convex Mirror (example) principal axis F • C •

Convex Mirror (example) principal axis F • C • The first ray comes in parallel to the principal axis and reflects through the focal point.

Convex Mirror (example) principal axis F • C • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis.

Convex Mirror (example) principal axis F • C • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. The light rays don’t converge, but the sight lines do.

Convex Mirror (example) principal axis F • C • The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. The light rays don’t converge, but the sight lines do. A virtual image forms where the sight lines converge.

Your Turn (Convex Mirror) object F • C • principal axis convex mirror Note: you just draw a line to represent thin mirrors Locate the image of the arrow

Your Turn (Convex Mirror) object image F • C • principal axis convex mirror Note: you just draw a line to represent thin mirrors Locate the image of the arrow

Mirror Equation ƒ = focal length p = object distance q = image distance f is negative for convex mirrors and concave lenses. f is negative for diverging mirrors q is negative when the image is behind the mirror

Magnification Equation M = magnification h’ = image height h = object height If height is negative the image is upside down if the magnification is negative the image is inverted (upside down)

Sign Conventions for Magnification Orientation of image with respect to object Sign of M Type of image this applies to Upright + virtual inverted - real

Rules for Drawing Reference Rays Line drawn from object to mirror Line drawn from mirror to image after reflection 1 Parallel to principal axis Through focal point F 2 3 Through center of curvature C Back along itself through C

Sign Conventions

Sample Problem B A concave spherical mirror has a focal length of 10.0 cm. Locate the image of a pencil that is placed upright 30.0 cm from the mirror. Find the magnification of the image. Draw a ray diagram to confirm your answer.               The image appears between the focal point (10.0 cm) and the center of curvature (20.0 cm) The image is real, smaller than the object, and inverted ( -1 < M < 0 )

Concave Mirror (example) 3       1         2   principal axis C • F •   2 3 1 The first ray comes in parallel to the principal axis and reflects through the focal point. The second ray comes through the focal point and reflects parallel to the principal axis. The third ray comes through the center of curvature and reflects back on itself.

Sample Problem C An upright object is placed in front of a convex spherical mirror with a focal length of 8.00 cm. An erect image 2.50 cm tall is formed 4.44 cm behind the mirror. Find the position of the object, the magnification of the image, and the height of the object. Draw a ray diagram to confirm your answer.                    

Spherical Aberration No clear focusing of the incident rays occurs when parallel rays far from the principal axis converge away from the mirror’s focal point

Parabolic mirrors offer excellent correction of spherical aberration Paraboloid

Reflecting Telescope or objective mirror Reflecting telescopes use parabolic mirrors (Cassegrain reflector)

Science Week Project Divide into groups of 3. Select a Physics topic for the project. Project group list and selected topic is due Monday 30/3/15. Submit via email to: hanan@atakamul.edu.kw Work as a group on a poster, a model, and power point presentation. All group members must be ready for presenting. This will be considered a lab for quarter 4. 11-3 Properties of Waves