PHY132 Introduction to Physics II Class 7 – Outline: Ch. 23, sections 23.6- 23.8 The Thin Lens Equation The Lens-Maker's Equation Image Formation with.

PHY132 Introduction to Physics II Class 7 – Outline:

• Ch. 23, sections 23.6-23.8

• The Thin Lens Equation

• The Lens-Maker's Equation

• Image Formation with Spherical Mirrors

Slide from http://hyperphysics.phy-astr.gsu.edu/hbase/vision/colcon.html

Response Curves for the three types of cones in the retina of the human eye.

Additive Primary Colours (light bulbs)and Subtractive Primary Colours (ink)

Why the Sky Is BlueFor small scattering particles, like nitrogen or oxygen molecules, higher frequency blue light is scattered much more readily than lower frequency red light.

Why the Sky Is Blue

𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦

If molecules in the sky scattered orange light instead of blue light, the sky would be

A. orange.

B. yellow.

C. green.

D. blue.

Why Sunsets Are RedCHECK YOUR NEIGHBOUR

Why Sunsets Are RedLight that is least scattered is light of low frequencies, which best travel straight through air.

If molecules in the sky scattered orange light instead of blue light, sunsets would be

A. orange.

B. yellow.

C. green.

D. blue.

Why Sunsets Are RedCHECK YOUR NEIGHBOUR

Image formation at a spherical interface

R is positive means surface is convex toward the objectR is negative means surface is concave toward objectso is positive means object is to the left of interfacesi is positive means image is real, to the right of interface

n1

so

n2

si

n2 n1

R

so si

Lensmaker’s Formula

so2si2

so1si1

1

so1

1

si2

(nl 1)1

R1

1

R2

Converging Lens

Focal Point

Focal length, f

NOTE: Focal length is defined for initially parallel rays.

Diverging Lens

Virtual Focal Point

Negative Focal length, −f

Rays appear to emerge from Virtual Focal Point

You can use the sun’s rays and a lens to start a fire. To do so, you should use

QuickCheck 23.8

A. A converging lens.

B. A diverging lens.

C. Either a converging or a diverging lens will work if you use it correctly.

Focusing Power Traditionally, lenses are specified not by

their focal length, but by the inverse of their focal length.

This is called “focusing power”

𝑃=1𝑓

The S.I. unit of focusing power is m–1 Traditionally, this unit is called the

“diopter,” abbreviated D.

1 D=1m− 1

Diverging rays through a Converging Lens

Focal length, f

If an object emits rays at the focal point, they end up being parallel on the other side of the converging lens.

What will happen to the rays emerging to the right of the lens if the face is moved a little closer to the lens?

A. They will remain parallel.B. They will diverge (spread out).C.They will converge (toward a focus).

f

What will happen to the rays emerging to the right of the lens if the face is moved a little closer to the lens?

B. They will diverge (spread out).

f

What will happen to the rays emerging to the right of the lens if the face is moved a little further away from the lens?

A. They will remain parallel.B. They will diverge (spread out).C.They will converge (toward a focus).

f

What will happen to the rays emerging to the right of the lens if the face is moved a little farther away from the lens?

B. They will converge (toward a focus).

f

Diverging rays through a Converging Lens

Focal length, f

s s’

fss

1

'

11Thin Lens Equation:

Thin Lens Equation: sign conventions

s s’

fss

1

'

11f

object image

s is positive for objects to the left of lens, negative for objects to the right of lens (virtual objects).

s’ is positive for images to the right of lens, negative for images to the left of lens (virtual images).

f is positive for converging lenses, negative for diverging lenses.

Example

• A lens has a focal power of +10 D.

• A 1 cm high object is placed 15 cm in front of the lens.

• Where does the image form?

+10D

s = 15 cm1 cm

A lens produces a sharply focused, inverted image on a screen. What will you see on the screen if a piece of dark paper is lowered to cover the top half of the lens?

A. An inverted but blurry image.

B. An image that is dimmer but otherwise unchanged.

C. Only the top half of the image.

D. Only the bottom half of the image.

E. No image at all.

QuickCheck 23.10

Lateral Magnification

• The absolute magnitude of the magnification |M | is defined to be the ratio of image height to object height.

• A positive value of M indicates that the image is upright relative to the object. A negative value of M indicates the image is inverted relative to the object.

• Note that when s and s’ are both positive, M is negative.

s

sM

h

hM

Example

• A lens has a focal power of +10 D.

• A 1 cm high object is placed 15 cm in front of the lens.

• How large is the image, and is it upright or inverted?

+10D

s = 15 cm1 cm

Ray TracingWith a converging thin lens

Ray TracingWith a diverging thin lens

The figure shows a concave mirror, a mirror in which the edges curve toward the light source.

Rays parallel to the optical axis reflect and pass through the focal point of the mirror.

Image Formation with Concave Spherical Mirrors

𝑓 =𝑅2

This focus only exists for rays that are close to the axis.

No good focusThis is called “spherical abberation”

A Real Image Formed by a Concave Mirror

The figure shows parallel light rays approaching a mirror in which the edges curve away from the light source.

This is called a convex mirror.

The reflected rays appear to come from a point behind the mirror.

Image Formation with Convex Spherical Mirrors

A Real Image Formed by a Convex Mirror

For a spherical mirror with negligible thickness, the object and image distances are related by:

where the focal length f is related to the mirror’s radius of curvature by:

The Mirror Equation

Midterm Test 1• Tuesday, Jan. 27, from 6:00pm to 7:30pm. Tomorrow!• The test will actually begin at 6:10pm and last for 80

minutes; please arrive 10 minutes early if you can, so you can get settled

• This test will count for 15% of your mark in the course• There will be no make-up for this test. Students who miss

a test for legitimate and documented reasons will have the weight of the test transferred to the other test which will then count for 30% of their course mark

• You must go to the correct room, based on your Practical Group

• Your practical group is the one that shows under the "My PRA groups" link on the Portal

“Which room am I in on Tuesday at 6:00pm?”

• EX = Exam Centre, 255 McCaul St.

• HA = Haultain Building, 170 College St.

Midterm Test 1• The test will have:

12 multiple-choice questions worth 5 points each (total = 60)

Two long-answer problems counting for a total of 40 points, which will be graded in detail; part marks may be awarded, but only if you show your work.

• Please bring: Your student card. A calculator without any communication capability. A pencil with an eraser. A single, original, handwritten 8 1/2 × 11 inch sheet of

paper on which you may have written anything you wish, on both sides.

Midterm Test 1 - hints• Don’t be late. If you’re very early, just wait outside the

room.

• Spend the first 2 or 3 minutes skimming over the entire test from front to back before you begin. Look for the easy problems that you have confidence to solve first.

• Before you answer anything, read the question very carefully. The most common mistake is misreading the question!

• Manage your time; if you own a watch, bring it. 10 problems over 80 minutes means an average of 8 minutes per problem.

• You CANNOT HAVE YOUR PHONE with you or in your pocket at a test or exam at U of T – you must store it in your backpack at the edge of the room, or in a special bag underneath your desk

Midterm Test 1 – more rules• You are also allowed a paper dictionary as an aid – ie it

could be a translation dictionary between your first language and English – the invigilator may flip through it to make sure no extra physics-stuff is written in there

• Bags, books pencil cases and ALL notes are to be deposited in areas designated by the Chief Presiding Officer and are not to be taken to the examination desk or table. If pencil cases are found on desks, they will be searched.

• If you bring a bag (paper, transparent plastic or non-transparent plastic), the following items may be stored inside it under your chair (as long as the bag is large enough): cell phone, wallet, laptop computer.

What will the test cover?

• Test 1 covers:– Knight Chapters. 20, 21, 22, 23

• If it’s in the above reading, on MasteringPhysics, done in classes, or done in Practicals, it is material that is important and that you should know for the tests and final exam.

Where to get help• Your classmates: go on Piazza.com, form a study group,

hang out in MP125, etc• Your two graduate student TAs. Learn their email

address, office hours, and office location.• Me. After class + MP121B office hours are T12, F10,

email [Note I am away Friday Jan.23]• Professor Meyertholen, MP129A office hours are M2,

F11-12• The Physics Drop-In Centre in MP125, back corner

MTWR 12-3, F11-2• Academic Success Centre in Koffler 1st floor, inside the

Career Centre

You see an upright, magnified image of your face when you look into magnifying “cosmetic mirror.” The image is located

Clicker Question

A. In front of the mirror’s surface.B. On the mirror’s surface. C. Behind the mirror’s surface.D. Only in your mind because it’s a virtual image.

Before Class 8 on Wednesday• Please read Knight Pgs. 720-736:

Ch. 25, sections 25.1-25.4• Note there is no pre-class reading quiz due

Wednesday, as it is the morning after the test.

• Something to think about: If you rub a balloon on your head, it becomes negatively charged. Where does this charge come from? Does your hair also become negative, or does your hair become positive?