Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign...

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Mirrors and Lenses

Transcript of Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign...

Page 1: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

Page 2: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Flat Mirrors

Images Formed by Spherical Mirrors

Concave Mirrors and Sign Conventions

Thin Lenses

Mirrors and Lenses

Sections 1-4

Page 3: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

The image formed by a plane mirror is upright, identical in size to the object, and as far behind the mirror as the object is in front of it.

Flat Mirrors

Page 4: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

The magnification is given by:

For a plane mirror, M = +1.

Flat Mirrors

Page 5: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Flat Mirrors

What length is required for a full length mirror?

A

B

2A

2B

Page 6: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Flat Mirrors

Multiple Images

Page 7: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Flat Mirrors

Multiple Images

1n360o

Page 8: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

A spherical mirror is a section of a sphere. It may be concave or convex.

Images Formed by Spherical Mirrors

Page 9: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Concave Mirror

Principle Focal Point 2R

f

Images Formed by Spherical Mirrors

Page 10: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A light ray, traveling parallel to a concave mirror's axis, strikes the mirror's surface near its midpoint. After reflection, this ray

(A) again travels parallel to the mirror's axis.

(B) travels at right angles to the mirror's axis.

(C) passes through the mirror's center of curvature.

(D) passes through the mirror's focal point.

Page 11: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Concave Mirror

Light Source at the Focal Point

Produces Parallel Rays of Light

Images Formed by Spherical Mirrors

Page 12: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A light ray, traveling obliquely to a concave mirror's surface, crosses the axis at the mirror's focal point before striking the mirror's surface. After reflection, this ray

(A) travels parallel to the mirror's axis.

(B) travels at right angles to the mirror's axis.

(C) passes through the mirror's center of curvature.

(D) passes through the mirror's focal point.

Page 13: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

We use ray diagrams to determine where an image will be. For mirrors, we use three key rays, all of which begin on the object:

1. A ray parallel to the axis; after reflection it passes through the focal point

2. A ray through the focal point; after reflection it is parallel to the axis

3. A ray perpendicular to the mirror; it reflects back on itself

Images Formed by Spherical Mirrors

Page 14: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Images Formed by Spherical Mirrors

Page 15: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Concave Mirror

Real Image

Images Formed by Spherical Mirrors

Page 16: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

For a concave mirror, the type of image formed depends on the position of the object.

Images Formed by Spherical Mirrors

Page 17: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Concave Mirror

Virtual Image

Images Formed by Spherical Mirrors

Page 18: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 19: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 20: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 21: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 22: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

The spherical-mirror equation is valid for any object position:

Images Formed by Spherical Mirrors

Magnification:

o

i

o

id

d

h

hM

Page 23: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A object is placed between a concave mirror and its focal point. The image formed is

(A) virtual and inverted.

(B) virtual and erect.

(C) real and erect.

(D) real and inverted.

Page 24: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Images Formed by Spherical Mirrors (Problem)

A 2.2 cm object is placed 15.0 cm from a concave mirror with a radius of 25.0 cm. (work on board)A) Where is the image located? B) What is its height?

di = 75 cmh = -11 cm

Page 25: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

A mirror at an amusement park shows an upright image of any person who stands 1.4 m in front of it. If the image is three times the person’s height, what is the radius of curvature?

m 4.13 oi Mdd

io ddf

111

io

io

dd

ddor

f

m 2.4m 4.1

m 2.4m 4.1f

m 1.2

m 2.4 m 1.22f2r

o

i

d

d

h

hM

'

m 2.4id

Images Formed by Spherical Mirrors (Problem)

Page 26: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A light ray, traveling obliquely to a concave mirror's axis, crosses the axis at the mirror's center of curvature before striking the mirror's surface. After reflection, this ray

(A) travels parallel to the mirror's axis.

(B) travels at right angles to the mirror's axis.

(C) passes through the mirror's center of curvature.

(D) passes through the mirror's focal point.

Page 27: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

If you stand in front of a concave mirror, exactly at its focal point,

(A) you will see your image at your same height.

(B) you won't see your image because there is none.

(C) you will see your image, and you will appear smaller.

(D) you will see your image and you will appear larger.

Page 28: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Convex Mirror

Images Formed by Spherical Mirrors

Page 29: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

f

do di

Images Formed by Spherical Mirrors

Convex Mirror

Image will always be virtual

Page 30: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

If you stand in front of a convex mirror, at the same distance from it as its radius of curvature,

(A) you won't see your image because there is none.

(B) you will see your image at your same height.

(C) you will see your image and you will appear smaller.

(D) you will see your image and you will appear larger.

Page 31: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A single convex spherical mirror produces an image which is

(A) always virtual.

(B) always real.

(C) real only if the object distance is less than f.

(D) real only if the object distance is greater than f.

Page 32: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 33: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Images Formed by Spherical Mirrors

Page 34: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Problem Solving: Spherical Mirrors

1. Draw a ray diagram; the image is where the rays intersect.

2. Apply the mirror and magnification equations.

3. Sign conventions: if the object, image, or focal point is on the reflective side of the mirror, its distance is positive, and negative otherwise. Magnification is positive if image is upright, negative otherwise.

4. Check that your solution agrees with the ray diagram.

Images Formed by Spherical Mirrors

Page 35: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Images Formed by Spherical Mirrors (Problem)

A convex mirror (C = 90 cm) is used in your rearview mirror. Another car is 15 m from the mirror. (work on board)A) Where is the image located? B) What is its magnification?

di = -0.437 mM = 0.0291

DOT requires C b/w 89-165 cm

Page 36: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Thin lenses are those whose thickness is small compared to their radius of curvature. They may be either converging (a) or diverging (b).

Thin Lenses

Page 37: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

Lenses that are thicker at the center

(A) spread out light rays.

(B) bend light rays to a point beyond the lens.

(C) have no effect on light rays.

(D) reflect light rays back.

Page 38: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Double Convex Lens

Focal Point

Thin Lenses

Page 39: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Chapter 23 Mirrors and Lenses

A light ray, traveling parallel to the axis of a convex thin lens, strikes the lens near its midpoint. After traveling through the lens, this ray emerges traveling obliquely to the axis of the lens

(A) such that it never crosses the axis.

(B) crossing the axis at a point equal to twice the focal length.

(C) passing between the lens and its focal point.

(D) passing through its focal point.

Page 40: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Ray tracing for thin lenses is similar to that for mirrors. We have three key rays:

1. This ray comes in parallel to the axis and exits through the focal point.

2. This ray comes in through the focal point and exits parallel to the axis.

3. This ray goes through the center of the lens and is undeflected.

Thin Lenses

Page 41: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Thin Lenses

Page 42: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Real Image

Double Convex Lens

Thin Lenses

Page 43: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 44: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 45: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 46: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 47: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.
Page 48: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

For a diverging lens, we can use the same three rays; the image is upright and virtual.

Thin Lenses

Page 49: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Virtual Focal Point

Concave Lens

Thin Lenses

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Page 51: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Thin Lenses

Page 52: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

The thin-lens equation:

Magnification:

Thin Lenses

o

i

o

id

d

h

hM

Power:Lens power is measured in diopters, D.

1 D = 1 m-1

Page 53: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Double Convex Lens

Thin Lenses

Page 54: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

A convex lens has a focal length f. An object is placed between f and 2f on the axis. The image formed is located

(A) at 2f.

(B) between f and 2f.

(C) at f.

(D) at a distance greater than 2f from the lens.

Page 55: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Thin Lenses (Problem)

A converging lens has a focal length of 20.0 cm. (work on board)

a) Locate the images for object distances of 40.0 cm,

b) Locate the images for object distances of 20.0 cm.

c) Locate the images for object distances of 10.0 cm.

,

cm 40

infinity approaches

cm 20

Page 56: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Concave Lens

Virtual Image

Thin Lenses

Page 57: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Mirrors and Lenses

The images formed by concave lenses

(A) are always real.

(B) are always virtual.

(C) could be real or virtual; it depends on whether the object distance is smaller or greater than the focal length.

(D) could be real or virtual, but always real when the object is placed at the focal point.

Page 58: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

An object is placed 8 cm from a 20 cm converging lens. (work on board)A)What is the image distance? B)What is M? C)Type of image (real or virtual)?

Thin Lenses (Problem)

di = -13.33 cmM = 1.67Virtual

Page 59: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

In lens combinations, the image formed by the first lens becomes the object for the second lens (this is where object distances may be negative).

Thin Lenses

Page 60: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Review of Chapter

• Plane mirrors form virtual, upright, and unmagnified images.

•The object distance is equal to the image distance.

•The lateral magnification factor for all mirrors and lenses is:

• Focal length of a spherical mirror:

Page 61: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

Review of Chapter

• Spherical-mirror equation:

• Thin-lens equation:

Page 62: Mirrors and Lenses. Flat Mirrors Images Formed by Spherical Mirrors Concave Mirrors and Sign Conventions Thin Lenses Mirrors and Lenses Sections 1-4.

homework - 1

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Homework - 2

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Homework - 3

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Homework - 4

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homework - 5

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homework - 6

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