Geometric Optics

• This chapter covers how images form when light bounces off mirrors and refracts through lenses.

• There are two different kinds of images:– A real image is formed when light rays pass

through and diverge from the image point. – A virtual image is formed when the light rays

do not pass through the image point but appear to diverge from that point.

Geometric Optics

• We will define:– p as the object distance– q as the image distance– M as the magnification– h as the object height– h’ as the image height– f as the focal length

Flat Mirror

• The image is as far behind the mirror as the object is in front of the mirror (p = q)

• The image is unmagnified (h = h’), virtual, and upright

• The image has front-back reversal

Flat Mirrors

• Both the object (O) and the images (I1 and I2) create images in this two-mirror configuration.

Magnification

• There is a relationship between the object height and the image height which we call the Lateral Magnification, or just the Magnification.

h

h

htobjectheig

timageheighM

'

Spherical Mirrors – Concave

Spherical Mirror - Concave

• Here we see light rays from a very distant object reflect on a concave mirror. They meet at the focal point (F).

• The distance from the mirror to F is defined as the focal length (f).

• For spherical mirrors,

2

Rf

Spherical Mirrors – Convex

Spherical Mirror Equations

p

q

h

hM

'

Mirror Equation

Rqp

211

2

Rf And since,

fqp

111

• These are examples of ray diagrams for spherical mirrors.

• Compare the three rays in each diagram to the rules on your handout.

– Ray 1 is drawn from the top of the object parallel to the principal axis and is reflected through the focal point F

– Ray 2 is drawn from the top of the object through the focal point and is reflected parallel to the principal axis

– Ray 3 is drawn from the top of the object through the center of curvature C and is reflected back on itself

Boundary Refraction - curved surface

1221 nnnn

R

nn

q

n

p

n 1221

Boundary Refraction – flat surface

q

n

p

n 21

pn

nq

1

2

Thin Lenses• These are examples

of thin lenses.

• We will refer to the “biconvex” as a converging lens and the “biconcave” as a diverging lens in practice

21

111

1

RRn

f

• If the radius is different on each side of the lens, a special equation is used.

• This is called the Lens Maker Equation.

• The ‘n’ in the equation represents the index of refraction of the lens glass.

Lens Equations (for any type of thin lens)

Thin Lens Equation

fqp

111

p

q

h

hM

'

Magnification

Ray Diagrams for Lenses

Combinations of Thin Lenses

• If two lenses are used to form an image, the system can be treated in the following manner:– The position of the image from the first lens can be

calculated while ignoring the presence of the second lens.

– Then that image can be used as the object for the second lens.

– The image from the second lens is the final image position for the system.

• It is very important to remember the Sign Conventions for Thin Lenses when solving this type of problem.

Example 26.8