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You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

Physics 24 spreadsheets with Exam 3 scores are available now.

Exam average 75.0% (12 sections out of 12). Better! Scores ranged from a low of 13 to a high of 200 (12 students).

Physics 24 Exam 3 will be returned in recitation tomorrow. Please check that points were added correctly. Review the course handbook and be sure to follow proper procedures before requesting a regrade. Get your regrade requests in on time! (They are due by Thursday of next week.)

Caution: it’s the points in the spreadsheet that count, not the percent. Your points can go down if you miss boardworks!

Physics 24 schedule for the rest of the semester:

November 13 & 14: Lenses

November 18 & 19: Double Slit Interference

November 20 & 21: Thin Film Interference

December 2 & 3: Diffraction

December 4 & 5: Final Review

Monday, December 9, 10:30 am:

50 point all multiple choice End Material Test

(you already have your 8 free points)

200 point all problem Final Exam

You may take one, or both, or neither

Special Homework #8 is due tomorrow. Download and print it if you lost it.

Death Rays.

You must know when to run from Death Rays. Maybe skip for now.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

Archimedes invents Death Ray that sets enemy ships on fire!

Fishbane* and Mythbusters say it’s impossible!

*Author of text used through spring 2006.

MIT students set wooden “ships” on fire with death rays! Details here!

Death Rays.

You must know when to run from Death Rays.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

Refraction at Spherical Surfaces

Convex surface:

1

R

2

axis

C

F

f

na

nb>na

Geometry: a light ray parallel to the axis passes through F.

An extended object will form an image inside the nb medium.

1

Ray 1: parallel to the axis, through F.

Ray 3: through C.

2

R

axis

C

F

s

f

s’

na

nb>na

This image is real and inverted.

R

F

C

axis

f

na

nb>na

Geometry: a light ray parallel to the axis seems to have come from F.

An extended object will form an image inside the na medium.

Ray 1: parallel to the axis, through F.

Ray 3: through C.

R

F

C

axis

f

na

nb>na

The image is virtual and upright.

There are three different places to put the object. The different images formed are always virtual and upright.

We can use geometry to derive an equation relating the image and source positions, and an equation for the magnification.

axis

C

F

R

s

f

s’

na

nb

The equations in this section are excellent approximations if both the angles of incidence and refraction are small.

R is positive when it is in the medium into which the light propagates. R is negative when it is in the medium from which the light radiates.

- The image distance is positive when the image is in the medium into which the light propagates, and negative if it is in the medium from which the light radiates (virtual image).

The object distance is positive when the object is in the medium from which the light radiates (the usual case—a real object), and negative if on the side opposite to the light source (a virtual object).

These are really “the same” as for mirrors.

Example: a Jurassic mosquito is discovered embedded in an amber sphere which has an index of refraction of 1.6. The radius of curvature of the sphere is 3.0 mm. The mosquito is located on the principal axis and appears to be imbedded 5.0 mm into the amber. How deep is the mosquito really?

nb=1

na=1.6

The object is in the amber, so na=1.6 and nb=1.

R

The image is in the medium from which the light radiates so s’=-5.0 mm.

s

s’

Example: a Jurassic mosquito is discovered embedded in an amber sphere which has an index of refraction of 1.6. The radius of curvature of the sphere is 3.0 mm. The mosquito is located on the principal axis and appears to be imbedded 5.0 mm into the amber. What is the magnification?

nb=1

na=1.6

s=4 mm and s’=-5.0 mm.

na=1.6 and nb=1

R

s

s’

Death Rays.

You must know when to run from Death Rays.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

You must understand the differences between these two kinds of lenses, be able to draw ray diagrams for both kinds of lenses, and be able to solve the lens equation for both kinds of lenses.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

A lens in this section is taken to be a single object made of transparent material of refractive material n>1.

There are two surface boundaries. Light from an object incident on the first surface forms an image, which becomes the object for the second surface.

A thin lens is one for which the distance from the object to each of the two surfaces is the “same” (and the distance from the imageto each surface is the “same”).

This would NOT qualify as a thin lens.

For compatibility with older versions of Powerpoint, I will make my lenses look “hollow,” like this.

Powerpoint 2007 shades in the lens fairly easily, but I prefer to save in Powerpoint 2003 format for compatibility purposes.

There are several surface combinations from which we can make lenses. Here are three (there are more).

Converging and Diverging Lenses

Thin lenses can be converging or diverging.

The converging lens is thicker in the center. The diverging lens is thicker at the edges.

There are focal points on both sides of each lens. The focal length is the same whether light passes from left to right or right to left.

There are two surfaces at which light refracts. Our equations (provided later) “automatically” take care of this.

In your diagrams, simply draw the incident ray up to the center of the lens, then draw the refracted ray in its final direction.

Death Rays.

You must know when to run from Death Rays.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

Ray Diagrams for Converging Lenses

Ray 1 is parallel to the axis and refracts through F.

Ray 2 passes through F’ before refracting parallel to the axis.

Ray 3 passes straight through the center of the lens.

I

F’

F

O

The image is real and inverted. In this case, it is larger than the object.

Ray Diagrams for Diverging Lenses

Ray 1 is parallel to the axis and refracts as if through F.

Ray 2 heads towards F’ before refracting parallel to the axis.

Ray 3 passes straight through the center of the lens.

F

I

F’

O

The image is virtual and upright. It is smaller than the object.

Converging and Diverging Lenses

The image formed by a converging lens may be real, inverted, and either smaller or larger than the object. It may also be virtual, upright, and larger than the object. See this web page.

The image formed by a diverging lens is always virtual, upright, and smaller than the object. See the same web page.

Do these lens properties remind you of anything else you’ve studied recently?

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=48.0

Handy quick reference card from Dr. Hale:

http://web.mst.edu/~hale/courses/Physics24/Quick.Reference.Cards/mirror.lens.table.pdf

If Problem 12.30 is assigned:

the image is 80 times larger than the object.

The object is very close to the lens compared to the image.

A ray diagram will be difficult to draw!

Do your best; maybe just make a diagram suggesting

how the rays converge “far” from the lens

Death Rays.

You must know when to run from Death Rays.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

Sign Conventions for The Lens Equation

The focal length f is positive for converging lenses and negative for diverging lenses.

The object distance s is positive if the object is on the side of the lens from which the light is coming; otherwise s is negative.

The image distance s’ is positive if the image is on the opposite side of the lens from where the light is coming; otherwise s’ is negative. (If s’ is negative, is the image real?)

The image height y’ is positive if the image is upright and negative if the image is inverted relative to the object.

Example: an object is located 5 cm in front of a converging lens of 10 cm focal length. Find the image distance and magnification. Is the image real or virtual?

It’s just a coincidence that the image is located at F’.

F’

F

O

Image distance is 10 cm, image is on side of lens light is coming from, so image is virtual. M=2 so image is upright.

Death Rays.

You must know when to run from Death Rays.

Refraction at Spherical Surfaces.

You must be able to calculate properties of images formed by refraction at spherical surfaces.

Thin Lenses: Concave and Convex Lenses, Ray Diagrams, Solving the Lens Equation.

If Time Allows: Lens Combinations, Optical Instruments.

You should be aware of this useful information.

To determine the image formed by a combination of two lenses, simply...

…calculate the image formed by the first lens…

…then use the first lens image as the source (object) for the second lens.

There is no homework on lens combinations.

Skip to sign conventions.

For viewing very far objects. Object distance taken as infinity.

Newtonian-focus reflecting telescope

Eyepiece magnification:

Overall magnification:

Compound Microscope

Again has objective and eyepiece, but because it is for viewing very near objects it is very different from the telescope.

Mirrors

Lenses

The focal length f is positive for converging lenses and negative for diverging lenses.

When the object, image, or focal point is on the reflecting side of the mirror, the distance is positive.

The object distance s is positive if the object is on the side of the lens from which the light is coming; otherwise s is negative (and the object is virtual).

When the object, image, or focal point is “behind” the mirror, the distance is negative.

The image distance s’ and radius of curvature R are positive if the image is on the side of the lens into which the light is going; otherwise negative.

The image height is positive if the image is upright, and negative if the image is inverted relative to the object.

The image height is positive if the image is upright, and negative if the image is inverted relative to the object.

Here’s a more compact way of expressing the sign conventions all at once.

Object Distance. When the object is on the same side as the incoming light, the object distance is positive (otherwise is negative).

Image Distance. When the image is on the same side as the outgoing light, the image distance is positive (otherwise is negative).

Radius of Curvature. When the center of curvature C is on the same side as the outgoing light, R is positive (otherwise is negative).

“Image Distance. When the image is on the same side as the outgoing light, the image distance is positive (otherwise is negative).”

If the image distance is negative, can the image be real?

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