Physics 212 Lecture 26: Lenses.

Physics 212 Lecture 26, Slide Physics 212 Lecture 26, Slide 11

Physics 212Physics 212Lecture 26: Lecture 26: LensesLenses

Main Point 1

First, we used two principal rays to derive the lens equation , that the sum of the inverse object and image distances is equal to the inverse of the focal length of the lens. We determined that this equation holds for both converging and diverging lenses, if we follow the convention that converging lenses have positive focal lengths while diverging lenses have negative focal lengths. Real images, corresponding to positive image distances, are produced by converging lenses when the object distance is greater than the focal length. Virtual images, corresponding to negative image distances, are always produced by diverging lenses and also by converging lenses when the object distance is less than the focal length.


Main Point 2

• Second, we defined the magnification in terms of the ratio of the image size to the object size. Using the lens equation, we obtained the result that the magnification is equal to minus the focal length divided by the difference of the object distance and the focal length. The sign convention used is that a negative magnification indicates an inverted image while a positive negative magnification indicates an upright image. For all single lenses, real images are inverted and virtual images are upright.


Main Point 3

Finally, we used Snell’s law to derive the lensmaker’s formula that relates the focal length of the lens to the index of refraction and the radii of curvature of the surfaces.



Refraction

That’s all of the physics – That’s all of the physics – everything else is just geometry!everything else is just geometry!

Snell’s Lawn1sin(1) = n2sin(2)

11

22

nn11

nn22


airair waterwater

glassglass glassglass

CaseCase II CaseCase IIIIIn In Case ICase I light in light in airair heads toward a piece of glass with incident angle heads toward a piece of glass with incident angle ii

In In Case IICase II, light in , light in waterwater heads toward a piece of glass at the heads toward a piece of glass at the samesame angle. angle.

In which case is the light bent most as it enters the glass?In which case is the light bent most as it enters the glass?

II or or II II oror Same Same (A) (B) (C)(A) (B) (C)

ii ii

22

22 1.51.5

1.3


Checkpoint 1a

A converging lens is used to project the image of an arrow onto a screen as shown above.The image isA. real and upright B. real and invertedC. virtual and upright D. virtual and inverted


Checkpoint 1b

A converging lens is used to project the image of an arrow onto a screen as shown above.A piece of black tape is now placed over the upper half of the lens. Which of the following is true?A. Only the lower half of the object (i.e. the arrow tail) will show on the screenB. Only the upper half of the object (i. e. the arrow head) will show on the screenC. The whole object will show on the screen


Checkpoint 2What happens to the focal length of a converging lens when it is placed under water?A. increases B. decreases C. stays the same


objectobject

1) Draw ray parallel to axis1) Draw ray parallel to axisrefracted ray goes through focusrefracted ray goes through focus2) Draw ray through center2) Draw ray through centerrefracted ray is symmetricrefracted ray is symmetric

imageimage

You now know the position of the same point on the imageYou now know the position of the same point on the image

Recipe for finding image:Recipe for finding image:

ff

http://physics.bu.edu/~duffy/java/Opticsa1.html


Diverging Lens:Diverging Lens: Consider the case where the shape of the Consider the case where the shape of the lens is such that light rays parallel to the axis of the mirror lens is such that light rays parallel to the axis of the mirror are all “focused” to a common spot a distance are all “focused” to a common spot a distance ff in front ofin front of the mirror:the mirror:

ff


SS S’<0S’<0

f<0f<0

1 1 1

S S f

SMS

image is:image is:virtualvirtual

uprightuprightsmallersmaller

objectobject

imageimageff


Executive Summary - Lenses:Executive Summary - Lenses:

SS > > 2f2frealreal

invertedinvertedsmallersmaller

2f2f > > S > f S > f realreal

invertedinvertedbiggerbigger

ff > > S > 0S > 0 virtualvirtual

uprightuprightbiggerbigger

SS > > 00 virtualvirtual

uprightuprightsmallersmaller divergingdiverging ff

convergingconverging ff

1 1 1

S S f

SMS


nnairairnnlenslensThis is why you can make thinner glasses out This is why you can make thinner glasses out of special materials that have of special materials that have nn greater than greater than nnglassglass..

We can also see this from the “Lensmaker’s Formula”We can also see this from the “Lensmaker’s Formula”

Recall glass rod in oil demo – Recall glass rod in oil demo – nn was the same and you saw no refraction at all was the same and you saw no refraction at all


CalculationCalculation

Conceptual Analysis

Strategic Analysis

A magnifying glass is used to read the fine print on a document. The focal length of the lens is 10mm.

At what distance from the lens must the document be placed in order to obtain an image magnified by a factor of 5 that is NOT inverted?

Physics 212 Lecture 26: Lenses.

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