Chapter Reflection and Mirrors

Millions of light rays reflect from objects and enter our eyes – that’s how we see them! When we study the formation of images, we will isolate just a few useful rays: or Web Link: Reflection, Refraction & DiffractionReflection, Refraction & Diffraction

Reflection  i = incident angle  r = reflected angle measured from the normal A line  to the surface at the point of incidence  i =  r Law of reflection

Ex: glossy vs. flat paint

Plane (flat) mirrors Web Link: Plane mirror imagePlane mirror image To locate the image: 1) Draw 2 different rays leaving the same point. 2) Draw their reflections. 3) Extend the reflections behind the mirror. 4) The point where they meet locates the image. image objectmirror

There are two different types of images: Real image Light rays actually meet at that point Virtual image Light rays only appear to emanate from that point Which type do you get from a plane mirror ? For all plane mirrors:  Image is upright  Image is same size as object  object’s distance from mirror (d o ) = image’s distance from mirror (d i )  Right and left are reversed

How tall a mirror do you need to be able to see your entire body? Does it matter how far away from the mirror you stand?

Multiple Reflections ( 2 or more mirrors) object image Web Link: Multiple reflectionsMultiple reflections

Spherical Mirrors concave side convex side

Concave Spherical Mirrors principle axis (axis of symmetry) C R C = Center of Curvature R = Radius of Curvature Web Link: Spherical mirrors and lensesSpherical mirrors and lenses Parallel Rays (distant object): C F f F = focal point f = focal length Web Link: Concave MirrorConcave Mirror f = ½ R Concave mirror

Spherical Aberration Because of the spherical shape of the mirror, the outer rays don’t reflect through the focal point: F Web Link: Spherical aberrationSpherical aberration This creates a blurry image Can you think of two ways that this problem could be eliminated? Web Link: Circular vs. parabolic mirrorCircular vs. parabolic mirror

Convex Spherical Mirrors C R Web Link: Spherical mirrors and lensesSpherical mirrors and lenses Parallel Rays (distant object): f = -½ R Convex mirror Since it’s behind the mirror Web Link: Convex mirrorConvex mirror f F C

Locating Images: Ray Tracing The use of 3 specific rays drawn from the top of the object to find location, size, and orientation of the image For a Concave Mirror: Ray #1: Parallel to the axis Relects through F Ray #2: Through F Reflects parallel to axis Ray #3: Through C Reflects back on itself

Results: Ray Tracing for concave mirrors (in each case, draw in the 3 rays for practice) Object is in front of C: Image is always real, smaller, and inverted CF Object between C and F: Image is always real, larger, and inverted CF Object between F and mirror: Image is always virtual, larger and upright C F Ex: Makeup mirror

For a Convex Mirror: Ray #1: Parallel to the axis / Relects as if it came from F Ray #2: Heads toward F / Reflects parallel to axis Ray #3: Heads toward C / Reflects back on itself

Results: Ray Tracing for convex mirrors (draw in the 3 rays for practice) Wherever the object is: Image is always virtual, smaller and upright CF Web Link: Ray tracingRay tracing Ex: Car side mirrors  Convex mirrors widen the field of view  “Objects in mirror are closer than they appear”

The Mirror Equation works for both concave and convex mirrors: OR CF f dodo CF f dodo f = mirror’s focal length (+ for concave, - for convex ) d o = distance between object and mirror d i = distance between image and mirror The Mirror Equation + for in front of mirror (real) - for behind mirror (virtual)

What about the size of the image ?? h o = height of object h i = height of image m = magnification = h i /h o m>1 if the image is larger than object m<1 if the image is smaller than object The Magnification Equation m is - if the image is inverted m is + if the image is upright

80 cm Ex: The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the cat. 15 cm

80 cm 15 cm Ex: The mirror’s radius of curvature is 60 cm. Find the location, size and orientation of the image of the dog.

Chapter Refraction and Lenses

Refraction- the bending of a light ray as it passes from one medium to another glassair light slows down (v<c) Web Links: Photon in medium & vacuum, Marching band, RefractionPhoton in medium & vacuum Marching bandRefraction

c = speed of light in a vacuum v = speed of light in a particular medium Notes:  For any medium, n > 1  v = f varies for different media stays the same varies for different media Web Link: Refractive indexRefractive index

Ex: If the speed of light in glass is 1.97 x 10 8 m/s, calculate the index of refraction for glass.

n 1 = initial medium n 2 = final medium  1 = incident angle  2 = refracted angle Don’t forget to measure angles from The Normal

Notice: If n 2 >n 1 : light ray bends toward the normal If n 2 <n 1 : light ray bends away from the normal n 1 sin  1 = n 2 sin  2 Snell’s Law

Ex: air water 60 Find both the angle of reflection and the angle of refraction for this light ray incident upon water.

Total Internal Reflection Web Link: Total internal reflectionTotal internal reflection Critical Angle Examples: DiamondsFiber Optics

Ex: Find the critical angle for light traveling from water toward air.

Apparent Depth When viewed from another medium, objects appear to have a different depth than they actually do. This makes spearfishing very difficult!

When viewed from directly above: d= apparent depth d = actual depth n 1 = medium containing object n 2 = medium containing observer

Example of Apparent Depth:

Ex: 11 cm How far above the water does the cat look to the fish?

DispersionDispersion Index of refraction (n) depends slightly on wavelength () Red: longest lowest n Violet: shortest highest n bends the most Web Link: PrismPrism

Rainbows are a result of dispersion

Sometimes a double rainbow can be seen. This is caused by a second internal reflection.

Lenses Converging Lens Diverging Lens F F f f

Find the focal length of a converging lens by holding it up to a window. (See how far away from the lens you need to hold a piece of paper to focus the image on the paper.) Web Link: Spherical mirrors and lensesSpherical mirrors and lenses

Ray Tracing for Lenses Light passes through a lens There is a focal point on both sides of a lens Converging Lens: Ray #1: Parallel to the axis Refracts through F Ray #2: Through F Refracts parallel to axis Ray #3: Through Center of lens undeflected

Example: Camera

Example: Slide Projector

Example: Magnifying Glass Web Link: Ray tracing Ray tracing

Results: Ray Tracing for Converging Lenses (in each case, draw in the 3 rays for practice) Object distance > 2f: Image is real, smaller, and inverted FF2F Object between f and 2f: Image is real, larger, inverted FF2F Object between f and lens: Image virtual, larger, upright FF2F

Ray #1: Parallel to the axis on the left Refracts as if it came from F on the left Ray #2: Heads toward F on the right Refracts parallel to the axis on the right Ray #3: Through the center of the lens undeflected Web Link: Spherical mirrors and lensesSpherical mirrors and lenses Now, for Diverging lenses…… For a Diverging Lens:

2 Example: Glasses to correct nearsightedness

Results: Ray Tracing for Diverging Lenses (draw in the 3 rays for practice) No matter where the object is: Image is always virtual, smaller and upright FF Web Link: Ray Tracing Summary for Mirrors and Lenses Ray Tracing Summary for Mirrors and Lenses Web Link: Ray tracingRay tracing

For a lens, a real image is on the opposite side as the object The Thin Lens Equation These equations also work on lenses: The Magnification Equation But the variables are defined slightly differently now because………. For a mirror, a real image was on the same side as the object

Sign conventions for Lenses Focal length (f) + converging - diverging Object distance (d o ) + object on the left Image distance (d i ) + image on the right (real) - image on the left (virtual) Magnification (m) + upright - inverted

Ex: lens book 13cm If the image of the book is 5.0 cm below the lens, find the focal length of the lens.

Ex: A camera with a focal length of 50 mm takes a photograph of a 100 m tall building from 350 m away. How tall is the image on the film?

The Human Eye Web Links: Eye lens,Eye lens Vision and Eyesight Near Point – Closest distance the eye can focus on (about 25 cm when we are young) Far Point – Farthest distance the eye can focus on (should be  )

Someone who is Nearsighted cannot focus on far away objects. (Their far point is not at infinity.) Nearsightedness can be corrected with diverging lenses Here’s how it works

Ex: Without my contact lenses, I need to stand 35 cm or less from the TV in order to see it in focus. Find the focal length of the contact lenses that correct my vision.

Someone who is Farsighted cannot focus on objects too near. Farsightedness can be corrected with converging lenses Here’s how it works