Chapter 2 geometrical_optics_a

Optics – geometrical optics

Contents

Postulates of ray optics Optical components

-Mirrors

-Lenses

-Stops and pupils Matrix optics

Ray Optics Ray optics is the simplest theory of light Light is described by rays that travel in different optical

media in accordance with a set of geometrical rules Ray optics is also known as Geometrical Optics Useful for studying image formation

Ray Optics

QUANTUM OPTICS

ELECTROMAGNETIC OPTICS

WAVE OPTICS

GEOMETRICAL OPTICS

Postulates of Ray Optics

Light travels in the form of rays An optical medium is characterized by a quantity

called refractive index, which is the ratio of speed of light in free space to that in the medium

The optical path length,

The optical path length corresponds to the distance in vacuum equivalent to the distance transverse in the medium of index n.

The time taken by light to travel from point S to P is proportional to the optical path length

Fermat’s Principle- Light, in going from point S to P, traverses the route

having the smallest optical path length or shortest time. Derivative of OPL is zero.

- Governs the laws of refraction & reflection

Postulates of Ray Optics

Plane of Incident

Plane of Incidence Contains Normal Contains Incident Ray Contains Refracted Ray Is the Plane Shown in

the Drawing Angles

– Defined from Normal

Represent light waves as straight lines or rays

If incident (incoming) light wave hits surface of different material some light will

– be reflected back

– travel through and be refracted

Plane of Incident

Define a line, the normal, which is - to surface at point where the incident beam hits the surface

Angles relative to normal– Angle of incidence -1– Angle of reflection q1’– Angle of refraction q2 Plane containing incident

ray and normal is plane of incidence

Plane of Incident

Reflection & Refraction

Law of reflection: Reflected ray lies in plane of incidence and angle for reflection is equal to angle of incidence

Law of refraction: Refracted ray lies in plane of incidence and angle of refraction is related to angle of incidence by Snell’s law

n is dimensionless constant called index of refraction. Index of refraction, n for given medium is defined as


Exercise Use Fermat’s principle to derive the law of reflection and

law of refraction.


Reflection & RefractionExample of application of Snell’s law

Exercise A beam of collimated light traveling in air makes an angle of

30o to the normal of a glass plate. If the index of the glass is ng = 3/2, determine the direction of the transmitted beam within the plate.


The angle of incidence which causes the refracted ray to point directly along the surface is called the critical angle, qc

Angles larger than qc, no light is refracted, so we have total internal reflection (TIR)

For total internal reflection to occur n2 < n1– E.g. moving from water into air– Will not happen if moving from air into water

Dispersion

n depends on wavelength of light, except in vacuum

Beam consists of different wavelengths, rays are refracted at different angles and spread out – chromatic dispersion

White light consists of components of all the colors in visible spectrum with uniform intensities

Dispersion

Imaging First, Assume a Point Object

Spherical Wavefronts and Radial Rays Define Object Location Find Image Location Real or Virtual?

Next Assume an Extended Object Compute Magnification

Transverse, Longitudinal, Angular

Signs and definition Object Distance, s

– Positive to Left Image Distance, s’

– For Refraction

• Positive to Right

– For Reflection

• Positive to Left

B’

Imaging

Imaging

Real Image Rays Converge Can Image on Paper Solid Lines in Notes

Virtual Image Extended Rays Converge Dotted-Lines in notes

Real and Virtual Images

Planar Mirrors

Point Object Extended Object

q

q

A A’-s’s

q

A A’

B B’

h x x’‘

Planar Mirrors

x’=x m=x’/x=1Transverse Magnification

ds’=-ds mz=ds’/ds=-1

Longitudinal Magnification

q’=q ma=q’/q =1Angular Magnification

Image is Virtual (Dotted lines converge)Erect (m>0),Perverted (cannot rotate to object)but not distorted (|m|=|mz|)

Spherical Mirrors

CA A’

qq

a bg

s

s’

R

h

Small-Angle Approximation

R

h

s

h

s

h 2

'

Rss

2

'

11

Conjugate Planes

Exterior Angles of Trianglesg=a+q b=g+q a+b=2gTangents of Anglestan a=h/s, tan b = h/s’,tan g = h/R

Spherical Mirrors

AA’

ss’B

B’

Transverse Magnification

'

'tan

s

x

s

x

s

s

x

xm

''

ma= / b a =s/s’= |1/m|

x

x’q

q

Spherical Mirrors

2''---

------

s

s

ds

dsmz

Image isReal (Converging Rays),Inverted (m<0),Distorted (mz=-m2),but Not Perverted (sign(m)=sign(mz))

ma=b/a =s/s’= |1/m|

Transverse Magnification


Angular Magnification

s

s

x

xm

'' -==

Rss

2

'

11

0'

'22

s

ds

s

ds

Image Equation Differentiate2

''

s

s

ds

dsmz


Spherical Mirrors

FF’A’

Object at Infinity

Rss

2

'

11

Rs

2

'

1

fs

1

'

1Definition Application

fss

1

'

11

C

Exercise Show that a spherical mirror equation is applicable to a

planar reflecting surface. A one-inch tall candle is set three inches in front of a

concave spherical mirror having a one-foot radius. Describe the resulting image.

Science

Chapter 2 geometrical_optics_a