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Chapter 31: Images and Optical Instruments Reflection at a plane surface Image formation P P’ The reflected rays entering eyes look as though they had come from image P’. Light rays radiate from a point object at P in all directions. virtual image

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Reflection and refraction at a plane surface Image formation

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Reflection and refraction at a plane surface Image formation i (or s’) is the image distance s is the object distance: |s| =|i| Sign Rules: (1)Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative. (2) Sign rule for the image distance: When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance i ( or s’) is positive. Otherwise it is negative. (3) Sign rule for the radius of curvature of a spherical surface: When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative. s’

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Reflection at a plane surface Image formation Multiple image due to multiple Reflection by two mirrors h h’ m = h’/h=1 lateral magnification image is erect image is virtual

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Reflection at a plane surface Image formation When a flat mirror is rotated, how much is the image rotated?

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Reflection at a spherical mirror Concave and convex mirror

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Reflection at a spherical mirror Focal points at concave and convex mirror Focal point or focus: Point F at which rays from a source point are brought together (focused) to form an image. Focal length: Distance f from mirror where focus occurs. f=R/2 where R is the radius of a spherical mirror.

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Reflection at a spherical mirror Focal points at a concave mirror h d object image If s’

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Reflection at a spherical mirror Image of an extended object at a concave mirror Principle rays: Light rays that can be traced (more easily) from the source to the image: 1. Parallel to optical axis 2. Passing through the focal point 3. Passing through the center of curvature 4. Passing through the center of the mirror surface or lens real image

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Reflection at a spherical mirror Magnification of image at a concave mirror h h’ When s,s’ >0, m<0 inverted s/s’ 0 upright or erect

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Reflection at a spherical mirror Example with a concave mirror real image virtual image

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Reflection at a spherical mirror Example with a concave mirror

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Reflection at a spherical mirror Image at a convex mirror ss’ f f R s positive s’ negative (virtual image) R negative f negative

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Reflection at a spherical mirror Magnification of image at a convex mirror s’ For a convex mirror f < 0 m > 1 magnified m < 1 minimized m > 0 image upright m < 0 image inverted

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Refraction at a spherical surface Refraction at a convex spherical surface For small angles

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Refraction at a spherical surface Refraction at a concave spherical surface For a concave surface, we can use the same formula But in this case R < 0 and f < 0. Therefore the image is virtual.

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Refraction at a spherical surface Relation between source and image distance at a convex spherical surface s’ For a convex (concave) surface, R >(<) 0. Snell’s law

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Refraction at a spherical surface Example of a convex surface |s’|

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Refraction at a spherical surface Example of a concave surface |s’|

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Refraction at a spherical surface Example of a concave surface

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Refraction at a spherical surface Example of a concave surface

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Convex Lens Sign rules for convex and concave lens: Sign Rules: (1)Sign rule for the object distance: When object is on the same side of the reflecting or refracting surface as the incoming light, the object distance s is positive. Otherwise it is negative. (2) Sign rule for the image distance: When image is on the same side of the reflecting or refracting surface as the outgoing light, the image distance i (or s’) is positive (real image). Otherwise it is negative (virtual image). (3) Sign rule for the radius of curvature of a spherical surface: When the center of curvature C is on the same side as the outgoing light, the radius of the curvature is positive. Otherwise it is negative.

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Convex Lens Lens-makers (thin lens) formula surface 1 surface 2 Image due to surface 1: s’ 1 becomes source s 2 for surface 2: s 1 = s and s’ 2 = s’: s’ Parallel rays (s=inf.) w.r.t. the axis converge at the focal point R 1 >0R 2 <0

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Convex Lens Magnification s’ same as for mirrors

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Convex Lens Object between the focal point and lens A virtual image

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Convex Lens Object position, image position, and magnification real inverted image m < 1 real inverted image m >1 virtual erect image m >1

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Lens Types of lens

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Lens Two lens systems

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Lens Two lens systems (cont’d)

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Lens Two lens systems (cont’d)

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Lens Two lens systems (cont’d)

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Eyes Anatomy of eye

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Eyes Near- and far-sightedness and corrective lenses farsightedness nearsightedness

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Angular size h d In general the minimum distance d=d min ~25 cm at which an eye can see image of an object comfortably and clearly.

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Magnifying glass whenbut for human eye. the minimum distance at which an eye can see image of an object comfortably and clearly. virtual image s’ the eye is most relaxed s ii hihi h

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Microscope small Object is placed near F 1 (s 1 ~f 1 ). Image by lens1 is close to the focal point of lens2 at F 2. magnifier image ang. size ii

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Refracting telescope angular size of image by lens2; eye is close to eyepiece image height by lens1 at its focal point Image by lens1 is at its focal point which is the focal point of lens 2 image distance after lens1 magnifier

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Reflecting telescope

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Aberration sphereparaboloid

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Chromatic aberration

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Gravitational lens

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Exercises Problem 1 Solution x/2 (h-x)/2 h-x x What is the size of the smallest vertical plane mirror in which a woman of height h can see her full-length? The minimum length of mirror for a woman to see her full height h Is h/2 as shown in the figure right.

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Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)~~f 1 -d
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Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)~~
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Exercises Problem 2 (focal length of a zoom lens) I’ r0r0 Q f1f1 f 2 =-|f 2 | r’ 0 d (variable)~~
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