# 1 From Last Time… Lenses and image formation Object Image Lens Object Image Thurs. Sep. 17, 2009Physics 208, Lecture 5.

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1 From Last Time… Lenses and image formation Object Image Lens Object Image Thurs. Sep. 17, 2009Physics 208, Lecture 5

Thurs. Sep. 17, 2009Physics 208, Lecture 52 1) Rays parallel to optical axis pass through focal point. 2) Rays through center of lens are not refracted. 3) Rays through F emerge parallel to optical axis. Thin-lens approximation: Ray tracing F F Object Image Optical Axis Here image is real, inverted, enlarged

Thurs. Sep. 17, 2009Physics 208, Lecture 53 Making an image s’ s Object Image Image distance Object distance f f focal length How are all these related?

Thurs. Sep. 17, 2009Physics 208, Lecture 54 Question A magnifying glass of diameter 2 cm and focal length 5 cm is used to form an image of the sun. Approximately what is the image distance? A.0.2 cm B.1 cm C.2 cm D.2.5 cm E.5 cm

Thurs. Sep. 17, 2009Physics 208, Lecture 55 Image size vs object size: Magnification = M = Magnification Image height Image distance Object dist. Object height

Thurs. Sep. 17, 2009Physics 208, Lecture 56 Far away objects The moon is 3.8x10 8 m away, and 3.5x10 6 m diameter. I use a 1 m focal length lens to make an image of the moon. About what diameter is this image of the moon? A.0.5 cm B.1 cm C.2 cm D.10 cm E.1 m

Thurs. Sep. 17, 2009Physics 208, Lecture 57 Different object positions Image (real, inverted) Object Image (virtual, upright) These rays seem to originate from tip of a ‘virtual’ arrow.

Thurs. Sep. 17, 2009Physics 208, Lecture 58 Virtual images Virtual image can’t be recorded on film, Can’t be seen on a screen. But rays can be focused by another lens e.g. lens in your eye (focus on retina) e.g. lens in a camera (focus on film plane) Image (virtual, upright) These rays seem to originate from tip of a ‘virtual’ arrow. objects closer to a converging lens than the focal length form a virtual image

Thurs. Sep. 17, 2009Physics 208, Lecture 59 Do these rays come from real image, a virtual image, or an object? Can’t tell. Rays are exactly equivalent, and can be imaged by a lens in exactly the same way.

Virtual Image : thin-lens equation Thurs. Sep. 17, 2009Physics 208, Lecture 510 Image (virtual) Object Object distance s Focal length f ( >0 for converging lens ) Image distance s’ Object distance < focal length Negative image distance: image on same side as object

Thurs. Sep. 17, 2009Physics 208, Lecture 511 Object at near point – biggest it can appear when in focus Magnifying glass oo Object closer than focal point —Lens produces virtual image Light rays appear to originate from virtual image Virtual image is used as object for eye lens. Have moved object ‘closer’, while permitting eye to focus  Image (virtual, upright) s s’

Thurs. Sep. 17, 2009Physics 208, Lecture 512 Magnifying glass A magnifying glass has a focal length of 8 cm. It is 1 cm in front of your eye. What is the closest that you can hold it to a bug so that the bug is in focus (your eye has a near point of 25cm). A.4 cm B.6 cm C.8 cm D.12 cm E.25 cm 1cm s=?

Magnifying glass: angular magnification Without magnifying glass, object is biggest at near point, ~ 25 cm. Subtends angle With magnifier Object can be closer, at object distance s Subtends angle Angular magnification is Increases with decreasing obj. dist. Smallest obj. dist. is for image at near point: Thurs. Sep. 17, 2009Physics 208, Lecture 513

Thurs. Sep. 17, 2009Physics 208, Lecture 514 Diverging lens Optical Axis Then thin-lens equation can be used: ObjectImage Focal length defined to be negative

Thurs. Sep. 17, 2009Physics 208, Lecture 515 Virtual image and diverging lens Example: object at infinity Rays appear to originate from focal point. Result Object has been (virtually) transported to a new location

Thurs. Sep. 17, 2009Physics 208, Lecture 516 Object Nearsightedness I can’t focus on this This, I can see

Thurs. Sep. 17, 2009Physics 208, Lecture 517 Object Fixing nearsightedness

Thurs. Sep. 17, 2009Physics 208, Lecture 518 Reading glasses Without my glasses, my far point is about 25 cm. What is the weakest (longest focal length) corrective lens (located at my eye) would let me read a newspaper holding it 50 cm away? A.-25 cm B.+25 cm C.-50 cm D.+50 cm E.-100 cm F.+100 cm Lens should form a virtual image closer to my eye. I can focus on image only if it is less than 25 cm away. Weakest lens moves it least, so image distance = -25 cm.

Diopters Two lenses close together ~ Single lens, “effective” focal length f eff Lens power P Defined as with f in meters Units of P are diopters Two lenses close together Thurs. Sep. 17, 2009Physics 208, Lecture 519

Thurs. Sep. 17, 2009Physics 208, Lecture 520 Far away objects The moon is 3.8x10 8 m away, and 3.5x10 6 m diameter. I use a 1 m focal length lens to make an image of the moon. About what diameter is this image of the moon? A.0.5 cm B.1 cm C.2 cm D.10 cm E.1 m Not a very big image. How can It be made ‘bigger’? Look at the image with a magnifying glass!

Thurs. Sep. 17, 2009Physics 208, Lecture 521 Telescope: two lenses, object far away Eyepiece forms virtual image Real image formed on retina by your eye lens. Objective: Forms real image of far-away object Eyepiece: Used as magnifying glass to examine image Eyepiece Objective

Telescope angular magnification Without telescope, distant planet subtends angle Objective lens forms real image Height Used as object by eyepiece lens Eyepiece Forms virtual image at infinity (for relaxed eye) Object must be at focal point Subtends angle Angular mag: Thurs. Sep. 17, 2009Physics 208, Lecture 522

Thurs. Sep. 17, 2009Physics 208, Lecture 523 Virtual image ‘Object’ Eyepiece Compound Microscope q p Object Real, inverted, image Objective Object outside focal point Forms a real image Real image used as object for eyepiece. Eyepiece forms virtual image for eye.

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