Optics Reflection and Refraction Mirrors and Lenses Chapter 17 and 18

Historical debate on nature of light Particles or Waves Light = EM waves

What is Light? - Revisited Wave-particle duality Quantum Optics Lasers LASER Stimulated emission Paradoxes in physics (BB radiation/ photoelectric effect) Quantisation of light (photons) E=hν Bohr model of atom Wavefunctions / Probability Diffraction of electrons Planck / Einstein Michelson Maiman (Laser) …

Fundamentals of Optics REFLECTION REFRACTION IMAGING DIFFRACTION INTERFERENCE POLARISATION Continuum of waves Finite no. of waves EM-theory

Refraction, Reflection, and Diffraction http://www.acoustics.salford.ac.uk/schools/teacher/lesson3/flash/whiteboardcomplete.swf Reflection – Waves bounce off a surface Refraction- Waves bend when they pass through a boundary Diffraction- Waves spread out (bend) when they pass through a small opening or move around a barrier.

Reflection When a wave encounters a barrier, it can reflect or the bounce off of the obstacle. Examples: Light – Mirrors Sound - Echo Most objects we see reflect light rather than emit their own light. Fermat's principle - light travels in straight lines and will take the path of least time A B Wrong Path True Path MIRROR

Law of Reflection The Law of Reflection states :The angle of incidence equals the angle of reflection. θi = θr This is true for both flat mirrors and curved mirrors.

Specular vs. Diffuse Reflection The Law of Reflection is Always Observed (regardless of the orientation of the surface) If the Law of Reflection is always observed, why do some objects seem to reflect light better than others? In diffuse reflection, waves are reflected in many different ways from a rough surface (you can’t see your refection) In specular reflection, waves are reflected in the same direction from a smooth surface (you can see your reflection)

Specular reflection from metal Diffuse reflection from skin Calm water can provide for the specular reflection of light from the mountain creating an image of the mountain on the surface of the water.

Mirror Image We trace rays from the object The image formed by the plane mirror is called a virtual image The image is the same distance behind the mirror as the object is in front of it The object and the image are the same size

Refraction When one medium ends and another begins, that is called a boundary. When a wave encounters a boundary that is more dense, part of it is reflected and part of it is transmitted The frequency of the wave is not altered when crossing a barrier, but the speed and wavelength are. The change in speed and wavelength can cause the wave to bend, if it hits the boundary at an angle other than 90°.

Refraction for Light Waves For light waves, this bending as light enters the water can cause objects under water to appear at a different location than they actually are. n – index of refraction: n = speed of light in a vacuum/ speed of light in material The index of refraction gives the speed of light in a medium: Fish in the water appear closer and nearer the surface. n2= 1.0 θ2 n1= 1.33 θ1 Water

Apparent Depth The submerged object's apparent depth equals its true depth divided by the liquid's index of refraction: d' = d(n2/n1). Note: n2 is the index of refraction of the medium above the surface and n1 is the index of refraction of the medium below the surface. www.physics.gla.ac.uk/~johannes/optics_lecture/overheads03_1_2_4-5.pdf

Critical Angle At an interface, when light is going from a region of high refractive index (lower speed) to lower index (higher speed), the light is bent away from the normal If the angle of incidence gets great enough it will be bending away at 90o This is called the critical angle

Total Internal Reflection Once the angle of incidence is larger than the critical angle, the light cannot escape the higher index material This means that all the light is reflected from the surface back into the higher index material This is total internal reflection

Refraction for Sound Waves Sound waves bend when passing into cooler or warmer air because the speed of sound depends on the temperature of the air. Sound travels slower in cooler air so the sound waves below are bend toward the surface of the water where the air is cooler. Refraction for Water Waves Water waves bend when they pass from deep water into shallow water, the wavelength shortens and they slow down.

Thin Film Interference in Peacocks Iridescence of peacock feathers is caused by light reflected from complex layered surface

Thin Film Interference in Bubbles We see colors on clear soap bubbles due to a combination of refraction and interference

Thin Film Interference Rays 1 and 2 interfere Ray 1 suffers a phase change of 180 degrees

Non-Reflective Coatings What must be the thickness t of silicon oxide for zero reflection of light with a wavelength of 550 nm? Since the phase changes cancel, we need a one-half wavelength shift as Ray 2 travels the extra distance 2t: Shifted wavelength in SiO: λ’ = λ/n = 550 nm /1.45 = 379.3 nm 2t = (1/2)(379.3 nm) t = 94.8 nm Note: A half wavelength phase occurs when the reflected rays reflects from a medium with higher index of refraction

Lenses are used to focus light and form images Lenses are used to focus light and form images. There are a variety of possible types; we will consider only the symmetric ones, the double concave and the double convex.

Converging Lens Diverging Lens

A ray diagram uses three rays to find the height and location of the image produced by a lens. The three principal rays for lenses are similar to those for mirrors: The P ray—or parallel ray—approaches the lens parallel to its axis. The F ray is drawn toward (concave) or through (convex) the focal point. The midpoint ray (M ray) goes through the middle of the lens. Assuming the lens is thin enough, it will not be deflected. This is the thin-lens approximation.

Ray Tracing for Lenses

note: C = 2f, where f is the focal point

The thin-lens approximation and the magnification equation:

Sign conventions for thin lenses:

Thin Lens Combination

Example 1 Real image, magnification = −1 An object is placed 20 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image? Real image, magnification = −1

Example 2 An object is placed 5 cm in front of a converging lens of focal length 10 cm. Where is the image? Is it upright or inverted? Real or virtual? What is the magnification of the image? Virtual image, as viewed from the right, the light appears to be coming from the (virtual) image, and not the object. Magnification = +2

Spherical Mirrors A spherical mirror has the shape of a section of a sphere. If the outside is mirrored, it is convex; if the inside is mirrored, it is concave.

Spherical Mirrors Spherical mirrors have a central axis (a radius of the sphere) and a center of curvature (the center of the sphere). Text

Concave Mirror For a real object very far away from the mirror, the real image is formed at the focus For a real object close to the mirror but outside of the center of curvature, the real image is formed between C and f. The image is inverted and smaller than the object.

For a real object at C, the real image is formed at C For a real object at C, the real image is formed at C. The image is inverted and the same size as the object. note: C = 2f, where f is the focal point and C is the center of curvature For a real object between C and f, a real image is formed outside of C. The image is inverted and larger than the object

For a real object at f, no image is formed For a real object at f, no image is formed. The reflected rays are parallel and never converge. For a real object between f and the mirror, a virtual image is formed behind the mirror. The position of the image is found by tracing the reflected rays back behind the mirror to where they meet. The image is upright and larger than the object.

Convex Mirror For a convex mirror the image from a real object is always behind the mirror, smaller than the object, upright and virtual.

Summary of Mirrors Mirror equation: Focal length of a convex mirror Focal length of a concave mirror

Here are the sign conventions for concave and convex mirrors:

Example 1 An object is placed 30 cm in front of a concave mirror of radius 10 cm. Where is the image located? Is it real or virtual? Is it upright or inverted? What is the magnification of the image? di>0  Real Image m = − di / do = −1/5

Example 2 An object is placed 3 cm in front of a concave mirror of radius 20 cm. Where is the image located? Is it real or virtual? Is it upright or inverted? What is the magnification of the image? Virtual image, di <0 Magnified, |m| > 1, not inverted. m > 0

Diffraction Diffraction involves a change in direction of waves as they pass through an opening or around a barrier in their path. http://www.ngsir.netfirms.com/englishhtm/Diffraction.htm

Diffraction of Sound and Light Waves Sound waves bend around obstacles and bend when passing through an opening making it possible to hear sound outside an open door or behind an obstacle. Light waves also bend around obstacles and when passing through an opening creating a diffraction pattern on a screen.

Sources http://www.physics.mun.ca/~jjerrett/lenses/c onvex.html http://www.educypedia.be/education/physics opticslenses.htm pls.atu.edu/physci/physics/people/bullock/Phy sical_principles_2/Lectures/Chapter_26.ppt www.physics.umd.edu/courses/Phys263/wth/f all04/downloads/LectureNotes/