Lecture 36: FRI 17Lecture 36: FRI 17 APRAPRPhysics 2102Jonathan Dowling34.1–4: Geometrical opticsGeometrical opticsGeometrical OpticsGeometrical Optics• “Geometrical” optics (rough approximation): light rays(“particles”) that travel in straight lines.• “Physical” Classical optics (good approximation):electromagnetic waves which have amplitude and phase thatcan change.• Quantum Optics (exact): Light is BOTH a particle (photon)and a wave: wave-particle duality.Plane MirrorsPlane MirrorsLight rays reflect on a plane mirror,and produce a virtual image behindthe mirror.What’s a virtual image? It means thelight rays are NOT coming from areal point, there is no light where theimage appears.i= -p for a plane mirrorobjectimageRay Tracing Plane (Flat) Mirror• Draw Perpendicular Line to Mirror From Each Point.• Use θi=θr To Draw Reflected Rays to Eye. • Draw Two Rays From Object to Point on Mirror.• Extend Reflected Rays Behind Mirror to Find Virtual ImageRay Tracing Plane (Flat) MirrorImage distance is minus Object distance, do!=! –di , meansimage is behind (minus) the mirror and | do!|=!|di| meansimage is behind mirror same distance object is in front.Virtual image means no light actually is at the imagelocation (optical illusion).Magnification m!=! +1 means image has same height as object(|m|=1) and image is right-side up (m is plus).hohi=+ho!=!–dom!=!ho/hi!=! +1Spherical mirrorsSpherical mirrors• Focal point is at half the curvatuire radius: f= - r/2 .•Rays parallel to the axis, reflect through the focal point.• Rays hitting the mirror after going to the focal point, emerge parallel.• Rays going through the center of curvature, reflect back on themselves.Concave mirrors: r > 0 Convex mirrors: r < 0Images fromImages fromspherical mirrorsspherical mirrorsfip111=+Consider an object placed between the focalpoint and the mirror. It will produce a virtualimage behind the mirror.When the object is at the focal point theimage is produced at infinity.If the object is beyond the focal point, a realimage forms at a distance i from the mirror.Check the signs!!pim !=lateralmagnificationRay Tracing Concave Mirror: Image Outside Focal Point• Ray Through Focal Point Bounces into Horizontal• Image is Real (Light At Image), Inverted, and Shrunk (m=ho/hi is minusand |m|< 1) and do and di are both positive (to left)• Horizontal Ray Bounces Through Focal Point• Ray Through Center Bounces Straight Back At’cha! • Rays Cross at Image PointRay Tracing Concave Mirror: Image Inside Focal Point• Ray Through Focal Point Bounces into Horizontal• Image is Virtual (no light), Upright, and Enlarged (m=ho/hi is plus and > 1) And do = + and di = – are on opposite sides of mirror. • Horizontal Ray Bounces Through Focal Point• Ray Through Center Bounces Straight Back At’cha! • Project Behind Mirror to Cross at Virtual ImageRay Tracing Convex Mirror• Ray Towards Focal Point Bounces into Horizontal• Image is Virtual (no light), Upright, and Shrunk (m=ho/hi is plus and < 1) And do = + and di = – are on opposite sides of mirror. • Horizontal Ray Bounces Into Line of Focal Point• Ray Towards Center Bounces Straight Back At’cha! • Project Rays Behind Mirror Cross at Virtual ImageExampleExampleAn object 2cm high is located 10cm from a convex mirror with aradius of curvature of 10cm. Locate the image, and find its height.Focal length: f= r/2= -10cm/2= -5cm.Image position: 1/i=1/f-1/p= -1/5cm –1/10cm= -3/10cm i= - 10/3cm = -3.33 cm: the image is virtual.Magnification: m= -i/p= - (-3.33cm)/(10cm)=+0.33 (upright, smaller).If the object image is 2cm, the image height is 0.33 x 2cm=0.67 cm.Newton’s Reflecting TelescopeHubble, Hubble, Toil and TroubleHubble, Hubble, Toil and TroubleHubble mirror screw up: The centralregion of the mirror was flatter thanit should be - by just one-fiftieth ofthe width of a human hair. This isequivalent to only four wavelengths ofvisible light, but it was enough. Oneinsider said that the Hubble mirrorwas "very accurate, very accuratelythe wrong shape".A star seen with a groundtelescope and with “old” HubbleThe same star seenwith the “new” HubbleBefore and
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