PHYS1311 101706 bw

Slide1: 

Lenses and Mirrors

Slide2: 

Properties of Light Law of Reflection - Angle of Incidence = Angle of reflection Law of Refraction - Light beam is bent towards the normal when passing into a medium of higher Index of Refraction. Light beam is bent away from the normal when passing into a medium of lower Index of Refraction. Index of Refraction - Inverse square law - Light intensity diminishes with square of distance from source.

Slide3: 

Normal Law of Reflection   Angle of incidence () = angle of reflection () The normal is the ray path perpendicular to the mirror’s surface.

Slide4: 

Center of curvature - the center of the circle of which the mirror represents a small arc Principal axis - a radius drawn to the mirror surface from the center of curvature of the mirror - normal to mirror surface Focus - the point where light rays parallel to principal axis converge; the focus is always found on the inner part of the "circle" of which the mirror is a small arc; the focus of a mirror is one-half the radius Vertex - the point where the mirror crosses the principal axis Focal length - the distance from the focus to the vertex of the mirror Geometry of a Concave Mirror Focus Principal axis Vertex Focal length

Slide5: 

Index of Refraction As light passes from one medium (e.g., air) to another (e.g., glass, water, plexiglass, etc…), the speed of light changes. This causes to light to be “bent” or refracted. The amount of refraction is called the index of refraction.

Slide6: 

Imagine that the axles of a car represent wave fronts. If the car crosses from a smooth to a rough surface at an angle, one tire of the axle will slow down first while the other continues at normal speed. With one tire traveling faster the other, the car will turn in the direction of the slow tire. This is how refraction works. Refraction

Slide7: 

AIR GLASS / WATER Slower Propagating Speed Car ( Sand / Gravel )

Slide8: 

AIR GLASS / WATER Slower Propagating Speed Car ( Sand / Gravel )

Slide9: 

AIR GLASS / WATER Slower Propagating Speed NORMAL

Slide10: 

AIR GLASS / WATER Slower Propagating Speed NORMAL LIGHT BENDING TOWARDS THE NORMAL LIGHT RAY

Slide11: 

n2 AIR GLASS / WATER Slower Propagating Speed NORMAL LIGHT BENDING TOWARDS THE NORMAL n1 Snell's Law ( Next Slide )

Slide12: 

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

Slide13: 

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

Slide14: 

GLASS / WATER Car AIR Slower Propagating Speed ( Sand / Gravel )

Slide15: 

AIR Slower Propagating Speed GLASS / WATER NORMAL AGAIN, LIGHT BENDS TOWARDS THE NORMAL upon entering a region with slower speed. LIGHT RAY

Slide16: 

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

Slide17: 

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

Slide18: 

Slower Propagating Speed GLASS /WATER Car AIR ( Sand / Gravel )

Slide19: 

NOW LIGHT BENDS AWAY FROM THE NORMAL Slower Propagating Speed GLASS /WATER AIR LIGHT RAY NORMAL

Slide20: 

Optical axis - axis normal to both sides of lens - light is not refracted along the optical axis Focus - the point where light rays parallel to optical axis converge; the focus is always found on the opposite side of the lens from the object Focal length - the distance from the focus to the centerline of the lens Geometry of a Converging (Convex) Lens Optical axis Focus Focal length

Slide21: 

Focal Plane l1 l2 o i Geometry of a Simple Lens f Lens formula Linear Magnification Using the Gaussian form of the lens equation, a negative sign is used on the linear magnification equation as a reminder that all real images are inverted The focal plane is where incoming light from one direction and distance (object distance o greater than focal length) is focused.

Slide22: 

The image formed by a single lens is inverted.

Slide23: 

Focal length Focal Plane

Slide24: 

The Eye The eye consists of pupil that allows light into the eye - it controls the amount of light allowed in through the lens - acts like a simple glass lens which focuses the light on the retina - which consists of light sensitive cells that send signals to the brain via the optic nerve. An eye with perfect vision has its focus on the retina when the muscles controlling the shape of the lens are completely relaxed - when viewing an object far away - essentially at infinity.

Slide25: 

When viewing an object not at infinity, the eye muscles contract and change the shape of the lens so that the focal plane is at the retina (in an eye with perfect vision). The image is inverted as with a single lens - the brain interprets the image and rights it.

Slide26: 

Geometry is similar for a concave mirror - image is inverted.

Slide27: 

Geometry of a Concave Mirror Vertex Focal length Focal plane

Slide28: 

Types of Optical Telescopes

Slide29: 

Refracting Telescope Uses lens to focus light from distant object - the eyepiece contains a small lens that brings the collected light to a focus and magnifies it for an observer looking through it.

Slide30: 

The largest refracting telescope in the world is the at the University of Chicago’s Yerkes Observatory - it is 40 inches in diameter and 63 feet long.

Slide31: 

Reflecting Telescope The primary mirror focuses light at the prime focus. A camera or another mirror that reflects the light into an eyepiece is placed at the prime focus.

Slide32: 

Types of Reflecting Telescopes Each design incorporates a small mirror just in front of the prime focus to reflect the light to a convenient location for viewing.

Slide33: 

Mirror Position and Focus Animation Focus Inversion Animation The image from reflecting and refracting telescopes is inverted. The focus is adjusted by changing the secondary mirror position.

Slide34: 

The Keck Telescopes Largest in the world - on Mauna Kea in Hawaii. 36 hexagonal mirrors function as single 10-meter mirror.

Slide35: 

The Hubble Space Telescope is 43.5 ft long and weighs 24,500 lbs. Its primary mirror is 2.4 m (7 ft 10.5 in) in diameter. The Hubble Space Telescope

Refracting/Reflecting Telescopes: 

Refracting/Reflecting Telescopes Refracting Telescope: Lens focuses light onto the focal plane Reflecting Telescope: Concave Mirror focuses light onto the focal plane Almost all modern telescopes are reflecting telescopes. Focal length Focal length

Secondary Optics: 

Secondary Optics In reflecting telescopes: Secondary mirror, to re-direct light path towards back or side of incoming light path. Eyepiece: To view and enlarge the small image produced in the focal plane of the primary optics.

Slide38: 

Magnification Using Two Lenses - Refracting Telescope f1 = 0.5 m f2 = 0.1 m f1 = 0.5 m f2 = 0.3 m Refracting telescope - consists of two lenses - the objective and the eyepiece (ocular). Incident light rays (from the left) are refracted by the objective and the eyepiece and reach the eye of the person looking through the telescope (to the right of the eyepiece). If the focal length of the objective (f1) is bigger than the focal length of the eyepiece (f1), the refracting astronomical telescope produces an enlarged, inverted image: magnification = f1 /f2 Similar for a reflecting telescope.

Slide39: 

Reflecting telescopes are primary astronomical tools used for research: Lens of refracting telescope very heavy - must be placed at end of telescope - difficult to stabilize and prevent from deforming Light losses from passing through thick glass of refracting lens - must be very high quality and perfectly shaped on both sides Refracting lenses subject to chromatic aberration Refracting vs Reflecting Telescopes

Slide40: 

Lens and Mirror Aberrations SPHERICAL (lens and mirror) Light passing through different parts of a lens or reflected from different parts of a mirror comes to focus at different distances from the lens. Result: fuzzy image CHROMATIC (lens only) Objective lens acts like a prism. Light of different wavelengths (colors) comes to focus at different distances from the lens. Result: fuzzy image

Slide41: 

Focal point for blue light Focal point for red light Focal point for all light The problem The solution Simple lenses suffer from the fact that different colors of light have slightly different focal lengths. This defect is corrected by adding a second lens Chromatic Aberration in Lenses

Slide42: 

Simple lenses suffer form the fact that light rays entering different parts of the lens have slightly difference focal lengths. As with chromatic aberration, this defect is corrected with the addition of a second lens. One focal point for all light rays The problem The solution Spherical Aberration in Lenses

Slide43: 

Simple concave mirrors suffer from the fact that light rays reflected from different locations on the mirror have slightly different locations on the mirror have slightly different focal lengths. This defect is corrected by making sude the concave surface of the mirror is parabolic The Problem The Solution All light rays converge at a single point Spherical Aberration in Mirrors

Two Fundamental Properties of a Telescope: 

Two Fundamental Properties of a Telescope Resolution smallest angle which can be seen  = 1.22  / D The angular resolution of a reflecting telescope is dependent on the diameter of the mirror (D) and the wavelength of the light being viewed () Light-Collecting Area think of the telescope as a “photon bucket” The amount of light that can be collected is dependent on the mirror area A =  (D/2)2 These properties are much more important than magnification which is produced by placing another lens - the eyepiece - at the mirror focus. Astronomers do not look through telescopes with their eyes - a light gathering detector (for instance a camera) records the image which can later on be magnified to any desired size.

Angular Resolution: 

Angular Resolution The ability to separate two objects. The angle between two objects decreases as your distance to them increases. The smallest angle at which you can distinguish two objects is your angular resolution.

Slide46: 

Angular Resolution of Car Lights Animation The maximum angular resolution attainable by the human eye is about one arcminute - in other words two stars will appear distinct if they are separated by more than one arcminute - remember that Tycho Brahe produced the best naked eye star charts ever - had resolution of one arcminute.

Slide47: 

The angular resolution of a reflecting telescope is dependent on the diameter of its mirror Mirror Angular Resolution Animation and the wavelength of the light Wavelength Effect on Resolution

Light Gathering Ability: Size Does Matter: 

Light Gathering Ability: Size Does Matter 1. Light-gathering power: Depends on the surface area A of the primary lens / mirror, proportional to diameter squared: A = (D/2)2 D

Slide49: 

So: light collecting ability of a reflecting telescope is dependent on the area of the mirror Light Collecting Area Animation

Magnifying Power: 

Magnifying Power Magnifying Power = ability of the telescope to make the image appear bigger. The magnification depends on the ratio of focal lengths of the primary mirror/lens (Fo) and the eyepiece (Fe): M = Fo/Fe A larger magnification does not improve the resolving power of the telescope!

Slide51: 

Imaging use a camera to take pictures (images) Photometry  measure total amount of light from an object Spectroscopy use a spectrograph to separate the light into its different wavelengths (colors) Timing measure how the amount of light changes with time (sometimes in a fraction of a second) Uses of Telescopes