Chapter 34 Geometric Optics - Florida International …faculty.fiu.edu/~hebli/wp-content/uploads/2017/03/Chapter34.pdf5 cm. Use the graphical method ... Focal point and focal length

Chapter 34

Geometric Optics

Lecture by Dr. Hebin Li

PHY 2049, Dr. Hebin Li

Goals of Chapter 34

To see how plane and curved mirrors form images

To learn how lenses form images

To understand how a simple image system works


Reflection at a plane surface

Light rays from a point radiate in all directions

Light rays from an object point reflect from a plane mirror as though they came from the image point


Refraction at a plane surface

Light rays from an object at P

refract as though they came

from the image point P .


Image formation by a plane mirror

Object distance and image distance

Sign rule for s: when the object is on the

same side of the reflecting or refracting

surface as the incoming light, s is positive;

otherwise, it is negative

Sign rule for 𝑠′: when the image is on the

same side of the reflecting or refracting

surface as the outgoing light, 𝑠′ is positive;

otherwise, it is negative


Characteristics of the image from a plane mirror

The image is just as far

behind the mirror as the

object is in front of the

mirror.

𝑠 = −𝑠′

The lateral magnification is

m = y/y.

The image is virtual (no real

light rays reach the image),

erect, reversed, and the same

size as the object 1

𝑠+1

𝑠′= 0


A flat mirror is simple, but …

A flat mirror is the simplest imaging optics.

Yeah! So simple… but wait a minute…

https://www.youtube.com/watch?v=vBpxhfBlVLU

I love physics!


The image is reversed

The image formed by a plane mirror is reversed

back to front.


Image formed by two mirrors

The image formed by

one surface can be the

object for another

surface.

This property can lead

to multiple images.

Question: What if the angle is not 90o?


Example:

An extended object is placed in front of a flat mirror and an image

of the object is formed by the mirror. Which of the following

statements is incorrect?

(A)The image is erect.

(B) The image is a virtual image.

(C) The image is reversed left and right.

(D)The image has the same size as the object.


Spherical mirror with a point object

Sign for R: when the center of

curvature C is on the same side as the

outgoing light, the radius of curvature

is positive; otherwise, it is negative.


Focal point and focal length

The focal length is half of the mirror’s radius of curvature: f = R/2.

(Lateral magnification)


Image of an extended object

Figure below shows how to determine the position, orientation and height of the image.


Example:

A spherical, concave mirror has a radius of curvature of 30 cm. An object

of is 90 cm to the left of the vertex of the mirror. The length of the object is

5 cm. Use the graphical method (i.e. use principal rays) to find the location

and length of the image. Compare your results by computing the location

and length of the image using the object and image relationship equation.


Focal point and focal length of a convex mirror

For a convex mirror, R is negative.


Image formation by a convex mirror

The same equations

describe the object-

image relationship.

𝑓 = 𝑅/2


Graphical methods for mirrors

Four principal rays for concave and convex mirrors.

Four principal rays cross at the object and image.


Concave mirror with various object distances


Example:

Rear-view Mirror: A mirror on the passenger side of your car is convex

and has a radius of curvature with magnitude 18.0 cm.

(a)Another car is behind your car, 9.00 m from the mirror, and this car

is viewed in the mirror by your passenger. If this car is 1.5 m tall,

what is the height of the image?

(b)What is the image distance? The mirror has a warning attached that

objects viewed in it are closer than they appear. Why is this so?


Image of a point object at a spherical surface


Image of a point object at a spherical surface


Example:

A Spherical Fish Bowl: A small tropical fish is at the center of a

water-filled, spherical fish bowl 28.0 cm in diameter.

(a)Find the apparent position and magnification of the fish to an

observer outside the bowl. The effect of the thin walls of the

bowl may be ignored.

(b)A friend advised the owner of the bowl to keep it out of direct

sunlight to avoid blinding the fish, which might swim into the

focal point of the parallel rays from the sun. Is the focal point

actually within the pool?


Thin converging lens

When a beam of rays parallel to the axis passes through a lens and converge to a point, such as a lens is called a converging lens (or positive lens).

The points 𝐹1 and 𝐹2 are called focal points. The distance from a focal point to the center of lens is called focal length.

The focal length is positive for a converging (positive) lens.

Any lens that is thicker at its center than at its edges is a converging lens with positive f.


Image formed by a thin converging lens

A thin converging lens can form an image of an extended object.

The object-image relationship is described as1

𝑠+1

𝑠′=1

𝑓

The lateral magnification can be calculated as

𝑚 = −𝑠′

𝑠


Types of lenses

Shown below are various types of lenses, both converging and diverging.

Any lens that is thicker at its center than at its edges is a converging lens with

positive f ; and any lens that is thicker at its edges than at its center is a

diverging lens with negative f.


Thin diverging lens

A beam of parallel rays incident on a diverging lens diverges.

The focal length of a diverging lens is a negative quantity, so a diverging lens is also called a negative lens.

Any lens that is thicker at its edges than at its center is a diverging lens with negative f.

The object-image relationship is described by the same equation:

1

𝑠+

1

𝑠′=

1

𝑓

The lateral magnification can be calculated as

𝑚 = −𝑠′

𝑠


Graphical methods for lenses

We can determine the position and size of an image formed by a thin lens by using three principal rays.

A ray parallel to the axis

A ray through the center of the lens

A ray through (or proceeding toward) the first focal point


Example: image formation by a converging lens

Find the image position and magnification for an object at each of

the following distances from a converging lens with a focal length

of 20 cm:

(a)50 cm;

(b)40 cm;

(c)15 cm.


Example: image formation by a diverging lens

A thin diverging lens has a focal length of 20 cm. You want to use

this lens to form an erect, virtual image that is 1/3 the height of the

object.

(a) Where should the object be placed?

(b) Where will the image be?


The effect of object distance

The object distance can have a large effect on the image.

1

𝑠+1

𝑠′=1

𝑓𝑠′ =

𝑓𝑠

𝑠 − 𝑓


Example:

A lens forms an image of an object. The object is 16.0 cm from the

lens. The image is 12.0 cm from the lens on the same side as the object.

(a)What is the focal length of the lens? Is it converging or diverging?

(b)If the object is 8.50 mm tall, how tall is the image? Is it erect or

inverted?

(c)Draw a principal-ray diagram.


An image of an image

The image formed by the first lens can act as an object for the second lens.


Example:

A 1.20-cm-tall object is 50.0 cm to the left of a converging lens of local

length 40.0 cm. A second converging lens, this one having a focal length

of 60.0 cm, is located 300.0 cm to the right of the first lens along the

same optic axis.

(a)Find the location and height of the image (call it I1) form by the lens

with a focal length of 40.0 cm.

(b)I1 is now the object for the second lens. Find the location and height

of the image formed by the second lens.


Cameras

When a camera is in proper focus, the position of the electronic sensor

coincides with the position of the real image formed by the lens.

© 2016 Pearson Education Inc.


Camera lens basics

The focal length f of a camera lens is the

distance from the lens to the image when the

object is infinitely far away.

The effective area of the lens is controlled by

means of an adjustable lens aperture, or

diaphragm, a nearly circular hole with

diameter D.

Photographers commonly express the light-

gathering capability of a lens in terms of the

ratio f/D, called the

f-number of the lens:



The eye

The optical behavior of the eye is similar to that of a camera.



Defects of vision

A normal eye forms an image on

the retina of an object at infinity

when the eye is relaxed.

In the myopic (nearsighted) eye,

the eyeball is too long from front

to back in comparison with the

radius of curvature of the cornea,

and rays from an object at

infinity are focused in front of

the retina.



Nearsighted correction

The far point of a certain myopic eye is 50 cm in front of

the eye.

When a diverging lens of focal length f = −48 cm is worn

2 cm in front of the eye, it creates a virtual image at 50 cm that

permits the wearer to see clearly.



Farsighted correction

A converging lens can be used to create an image far enough away

from the hyperopic eye at a point where the wearer can see it clearly.



Angular size

The maximum angular size of an object viewed at a comfortable

distance is the angle it subtends at a distance

of 25 cm.



The magnifier

The angular magnification of a simple magnifier is:



The compound microscope



The astronomical telescope

The figure below shows the optical system of an astronomical

refracting telescope.



The reflecting telescope

The Gemini North telescope

uses an objective mirror

8 meters in diameter.


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Chapter 34 Geometric Optics - Florida International …faculty.fiu.edu/~hebli/wp-content/uploads/2017/03/Chapter34.pdf5 cm. Use the graphical method ... Focal point and focal length