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A equal angles B

Physics 116

Lecture 15 Mirrors and tracing Oct 24, 2011

R. J. Wilkes Email: [email protected] Announcements

•! Guest lecturer today: Prof. Victor Polinger Lecture Schedule (up to exam 2)

Today

3 Rays vs

•! We know travels in the form of electromagnetic waves •! We can picture light rays as lines perpendicular to the , indicating the direction the light is traveling

wavefronts

rays •! If light were a stream of particles (as Newton thought), rays would describe particle paths •! Ray (or geometric optics) is very convenient for analyzing optical systems that are very large compared to the of light

4 of light rays

•! Light rays reflected off a smooth surface (specular reflection) will obey the simple law

The angle of reflection = angle of incidence –! Both are measured relative to normal to surface at point of reflection

equal angles If the surface is not A smooth – light rays arriving at nearby Line normal to surface points get reflected at B very different angles – reflection will be diffuse

5 Reflection (Deep Thought)

•! Reflection law is also consistent with the “principle of least time” –! In going from point A to point B, reflecting off a mirror, the ray path actually traveled is also the fastest (shortest) route Distance traveled from A to B is longer for any other path •! Nature automatically finds the most economical path !

A

fastest path: longer equal angles B

6 Looking in the mirror

•! It’s helpful to think in terms of images Looking into a mirror, light rays appear to come from behind the mirror Actual incident ray Apparent path of ray line of sight to image’s head

h/2 real you

R R h Mirror need only “image” you be half as high as you are tall to see your whole body. Your image will appear same distance behind mirror as you are in front of it. 7 Plane Reflection: examples

•! Angle of incidence is 55 deg, find angle of 2nd reflection

•! What is the minimum value of h to see the tabletop in the mirror below?

8 Curved mirrors

•! What if mirror isn’t flat? –! Same rules, but must use local surface normal for ray •! Spherical mirrors focus parallel incoming parallel rays to a point –! Just as (we’ll soon see) a does for rays passing through it –! Parallel rays = rays coming from a very distant source (eg, a star)

C = center of curvature of mirror

Optic axis C f o o Ray through C is just reversed (symmetry axis of system)

f = focal point = halfway between C and mirror

9 diagrams

•! For mirrors (and ) we can use simple rules to trace the paths of certain rays –! C rays – rays that pass through the center of curvature of the mirror –! P rays – rays that are parallel to the optic axis of the mirror –! F rays – rays that pass through the focal point after (or before*) reflection * Deep thought: ray paths have “time-reversal” symmetry – work just as well backwards C = center of curvature of mirror f = focal point = halfway to C So f = R/2 P rays pass through F Optic axis C o o Any ray through C is just reversed f (symmetry axis of system)

10 Two kinds of images

•! Real image –! Rays of light from point on object actually converge on image plane •! You can “catch” a real image on a screen: object is “reconstructed” when rays from points on the object re-converge on image plane •! Examples: movie on theater screen, this slide on lecture-hall screen, images projected by a slide projector, or darkroom enlarger –! Real images can be captured directly on photo film or chip •! Virtual image –! Rays of light appear to come from image plane when viewed, but never actually converge in space •! You can view a virtual image, but cannot capture it on a screen (or film or video camera) –! Of course, a camera (lens system) can view it, and record it that way •! Examples: your image in bathroom mirror, image in a magnifying glass, image in a “Galilean” telescope –! You can only view virtual images by looking through the mirror or lens –! The image is an “optical illusion”: your brain reconstructs the rays as coming from the virtual image location 11 Real vs virtual

•! Concave mirror can form a real image if object is farther away than its focal length

object Image size =h’ Object size =h C f ’ h’ = Mh o o Here, M is negative Ray through C is just reversed image (inverted image)

–! Ray tracing diagram shows two rays, from tip of object (arrow) •! Ray passing through center of curvature is reflected on itself •! Ray arriving parallel to optic axis is reflected to pass through f –! Rays from any other point on object would converge on corresponding point on image –! Image formed is real and inverted –! Image is magnified: h’ = Mh (in this case, smallified !) •! Searchlight Mirror demo: object is almost at C •! Convex mirror images are always virtual 12 Virtual image

•! Spherical mirror forms virtual image if object is closer than f

object image

o o C f ’

–! Now, reflected rays never actually converge, but appear to converge if extended behind the mirror (appear to come from virtual image) •! Person viewing mirror would “see” magnified image behind it –! This is a “shaving mirror” or magnifying mirror –! You have to put your face close to it to see your magnified image •! Home experiment: Put shaving mirror on floor, facing up, and hold your hand above it while gazing into mirror: if f is right, you will see a real image of your hand apparently floating in space above the mirror! –! Looks spooky because you expect images in mirrors to be behind the glass, not in front.

13 Mirror equation

•! Euclid tells us how to find the relations between image, object and mirror locations for reflection, using the law of reflection, and ray tracing rules: it’s all about similar triangles

Works for convex mirrors also: Just remember, R is negative for them: f = – R/2

14 Examples

•! Object is placed 1.5R in front of concave mirror: what is image type, location, and magnification?

Minus means inverted; rays converge at image, so it is real •! Object is placed 1.5R in front of convex mirror: what is image type, location, and magnification?

Plus sign means erect image; rays appear to emerge from image, so it is virtual 15