Reflection and Mirrors

Chapter 17

Physics Principles and Problems

Zitzewitz, Elliot, Haase, Harper, Herzog, Nelson, Nelson, Schuler and Zorn

McGraw Hill, 2005

Law of Reflection

• The normal is the imaginary line that is draw perpendicular to the reflective surface.

• The angle between a reflected ray and the normal is equal to the angle between the incident ray and the normal (r = i).

http://www.etsu.edu/math/gardner/einstein/e-reflection.jpg http://spaceguard.iasf-roma.inaf.it/tumblingstone/issues/num8/light/img/reflection.gif

• Smooth surfaces produce specular reflection (parallel light rays are reflected in parallel).

• Rough surfaces produce diffuse reflection (parallel light rays are reflected in non parallel ways).

• Individual rays, however, in both cases still adhere to the laws of reflection.

http://www.lightandmatter.com/html_books/5op/ch01/figs/specular-and-diffuse-reflection.png

http://micro.magnet.fsu.edu/optics/lightandcolor/images/reflectionfigure2.jpg

Plane-Mirror Images• Object is the source

of light rays that are to be reflected (could be either luminous like a light-bulb, or illuminated like the rook).

• Light travels from object point to the mirror and is reflected. The brain processes this as if the light traveled in a straight path (thus creating a virtual image).

http://sol.sci.uop.edu/%7Ejfalward/reflection/castlemirror.jpg

Plane Mirror Image Position and Height

• The virtual image position is equal to the negative of the object position. The negative indicates that the image is virtual (di = -do).

• The virtual image height is equal to the object height

(hi = ho).

http://www.physics.brocku.ca/Courses/1P22_Crandles/images/f25007.jpg

Concave Mirrors

• Edges of mirror curve towards observer.• C = geometric center of sphere.• CP = line segment between C and P. Also equal to sphere’s

radius (r).• P = center of mirror where principle axis intersects the mirror.• F = focal point where reflected parallel rays converge.• f = is the position of the focal point with respect to the mirror (f = r/2).

http://www.vidyavahini.ernet.in/shishya/products/AcademicContent/CBSE/X/Physics/light/xlight_files/image001.gif

• The properties of an object’s real image (image that is formed from the convergence of light rays) are dependent upon the distance the object is from the concave mirror.

http://electron9.phys.utk.edu/optics421/modules/m1/images/concavreal.gif

• (a) If the object is more than twice the focal length, than the real image will be inverted and smaller.

• (b) If the object is twice the focal length, than the real image will be inverted.

• (c) If the object is less than twice the focal length, than the real image will be inverted and bigger.

• (d) If the object is the exact focal length that no real image will be seen.

• (e) If the object is less than the focal length a virtual image that is larger and upright is formed behind the mirror.

http://media.wiley.com/Lux/26/10326.nfg014.jpg

What do these two different pictures of concave mirrors tell you about the object’s position?

http://doflick.com/flash/thumbnails//University/Physics/REFLECTIONS_FROM_A_CONCAVE_MIRROR.jpg

http://www.monticello.org/gallery/innovations/concavemirror.jpg

These properties can be solved for using two different equations.

• Mirror Equation - the reciprocal of the focal length of a spherical mirror is equal to the sum of the reciprocals of the image position and the object position.

• 1 / f = 1 / di + 1 / do

• Magnification - the magnification of an object by a spherical mirror can be calculated by image height divided by the object height (which is equal to the negative of the image position divided by the object position).

• m = hi / ho = -di / do

Convex Mirrors

• Edges of reflective surface curve away from the observer.

• Focal point and center of sphere are behind the mirror.

• Object reflects a virtual image that is reduced in size.

http://electron9.phys.utk.edu/optics421/modules/m1/images/convex.gif

http://4blackbird.com/images/black.jpg