Objectives: After completing this module, you should be able to:

• Explain and discuss with diagrams, reflection, absorption, and refraction of light rays.

• Define and illustrate your understanding of real, virtual, erect, inverted, enlarged, and diminished as applied to images.

• Use geometrical optics to draw images of an object at various distances from converging and diverging mirrors.

• Illustrate graphically the reflection of light from plane, convex, and concave mirrors.

Geometrical Optics

In the study of how light behaves, it is useful to use “light rays” and the fact that light travels in straight lines.

When light strikes the boundary between two media, three things may happen: reflection, refraction, or absorption.

reflection

refraction

absorption Water

Air

Reflection, Refraction, and Absorption

Water

Air

Reflection: A ray from air strikes the water and returns to the air.

Refraction: A ray bends into the water toward the normal line.

Absorption: A ray is absorbed atomically by the water and does not reappear.

reflection

refraction

absorption Water

Air reflection

refraction

absorption

The Laws of Reflection

Water

Air 1. The angle of inci- dence qi is equal to the angle of reflection qr :

qi = qr

qi

N reflection

qr

All ray angles are measured with respect to normal N.

2. The incident ray, the reflected ray, and the normal N all lie in the same plane.

3. The rays are completely reversible.

The Plane Mirror

A mirror is a highly polished surface that forms images by uniformly reflected light.

Note: images appear to be equi-distant behind mirror and are right-left reversed.

Definitions

Object distance: The straight-line distance p from the surface of a mirror to the object.

Image distance: The straight-line distance q from the surface of a mirror to the image.

Object distance

Image distance

=

p = q

qi = qr

Object Image

p q

Real and Virtual

Real images and objects are formed by actual rays of light. (Real images can be projected on a screen.)

Virtual images and objects do not really exist, but only seem to be at a location.

Virtual images are on the opposite side of the mirror from the incoming rays.

Real object

Virtual image

Light rays No light

Image of a Point Object

Plane mirror

Real object

p

Image appears to be at same distance behind mirror regardless of viewing angle.

q Virtual image

q = p

Image of an Extended Object

Plane mirror

p q

Image of bottom and top of guitar shows forward-back, right-left reversals.

q = p

Virtual image

Terms for Spherical Mirrors

A spherical mirror is formed by the inside (concave) or outside (convex) surfaces of a sphere.

A concave spherical mirror is shown here with parts identified.

Concave Mirror

Radius of curvature R Vertex V

Center of Curvature C

The axis and linear aperture are shown.

Linear aperture

V

C

R Axis

The Focal Length f of a Mirror

axis

qr

qi

R

Incident parallel ray

f

The focal length, f

The focal length f is:

2

Rf

The focal length f is equal to half the radius R

Since qi = qr, we find that F is mid- way between V and C; we find: C V F

Focal point

For objects lo- cated at infinity, the real image appears at the focal point since rays of light are almost parallel.

The Focus of a Concave Mirror

The focal point F for a concave mirror is the point at which all parallel light rays converge.

axis

Incident parallel Rays

C F

Focal point 2

Rf

The Focus of a Convex Mirror

The focal point for a convex mirror is the point F from which all parallel light rays diverge.

axis C F

R

Incident Rays

Reflected Rays

Virtual focus; reflected rays diverge.

2

Rf

Image Construction:

Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror.

C F

Convex mirror

Object

C F

Concave mirror

Object

Ray 1 Ray 1

Image Construction (Cont.):

Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to the mirror axis.

Concave mirror

C F Ray 2

Ray 1

Image C F

Convex mirror

Ray 2

Ray 1

Image

Image Construction (Cont.):

Ray 3: A ray that proceeds along a radius is always reflected back along its original path.

C F

Convex mirror

Concave mirror

C F

Ray 2

Ray 1

Ray 3

Ray 3

C F

Ray 2

Ray 1

Image

The Nature of Images

An object is placed in front of a concave mirror. It is useful to trace the images as the object moves ever closer to the vertex of the mirror.

We will want to locate the image and answer three questions for the possible positions:

3. Is it enlarged, diminished, or the same size?

2. Is the image real or virtual?

1. Is the image erect or inverted?

Object Outside Center C

Concave mirror

C F

Ray 3

Ray 2

Ray 1 1. The image is inverted; i.e., opposite of the object orientation.

2. The image is real; i.e., formed by actual light rays in front of mirror.

3. The image is diminished in size; i.e., smaller than the object.

Image is located between C and F

Object at the Center C

C F

Ray 2

Ray 1 1. The image is inverted; i.e., opposite of the object orientation.

2. The image is real; i.e., formed by actual light rays in front of mirror.

3. The image is the same size as the object. Image is located

at C, inverted.

Ray 3

Object Between C and F

1. The image is inverted; i.e., opposite of the object orientation.

2. The image is real; i.e., formed by actual light rays in front of mirror.

3. The image is enlarged in size; i.e., larger than the object.

Image is outside of the center C

C F

Ray 1 Ray 3

Ray 2

Object at Focal Point

Image is located at infinity (not formed).

C

F

Ray 3

Reflected rays are parallel

When the object is located at the focal point of the mirror, the image is not formed (or it is located at infinity).

The parallel reflected rays never cross.

Ray 1

Object Inside Focal Point

1. The image is erect; i.e., same orientation as the object.

2. The image is virtual; that is, it seems to be located behind mirror.

3. The image is enlarged; bigger than the object.

Image is located behind the mirror

C

F Erect and enlarged

Virtual image

Convex Mirror Imaging

C F

Convex mirror

Ray 2

Ray 1

Image

All images are erect, virtual, and diminished. Images get larger as object approaches.

C F

Convex mirror

Ray 1

2

Image gets larger as object gets

closer

Converging and Diverging Mirrors

Concave mirrors and converging parallel rays will be called converging mirrors from this point onward.

Convex mirrors and diverging parallel rays will be called diverging mirrors from this point onward.

C F

Converging Mirror

Concave

C F

Diverging Mirror

Convex

Summary

Reflection: A ray from air strikes the water and returns to the air.

Refraction: A ray bends into the water toward the normal line.

Absorption: A ray is absorbed atomically by the water and does not reappear.

Water

Air reflection

refraction

absorption

Summary (Cont.)

Water

Air 1. The angle of inci- dence qi is equal to the angle of reflection qr :

qi = qr

qi

N reflection

qr

All ray angles are measured with respect to normal N.

2. The incident ray, the reflected ray, and the normal N all lie in the same plane.

3. The rays are completely reversible.

Summary (Definitions)

Object distance: The straight-line distance p from the surface of a mirror to the object.

Image distance: The straight-line distance q from the surface of a mirror to the image.

Real image: An image formed by real light rays that can be projected on a screen.

Virtual image: An image that appears to be at a location where no light rays reach.

Converging and diverging mirrors: Refer to the reflection of parallel rays from surface of mirror.

Image Construction Summary:

Ray 1: A ray parallel to mirror axis passes through the focal point of a concave mirror or appears to come from the focal point of a convex mirror.

Ray 2: A ray passing through the focus of a concave mirror or proceeding toward the focus of a convex mirror is reflected parallel to mirror axis.

Ray 3: A ray that proceeds along a radius is always reflected back along its original path.

Summary (Cont.)

For plane mirrors, the object distance equals the image distance and all images are erect and virtual.

For converging mirrors and diverging mirrors, the focal length is equal to one-half the radius.

All images formed from convex mirrors are erect, virtual, and diminished in size.

Except for objects located inside the focus (which are erect and virtual), all images formed by converging mirrors are real and inverted.