Introduction to Experiments in Optics

Damzen 09/07

Short Tutorial on Optics (PowerPoint)Safety & Good working practices

A. Lens Imaging (Ray Optics)

B. Single-slit diffraction (Wave Optics)

1st Yr Laboratory, Physics, Imperial College London

METRO WAN

METRO WAN

TRANS-OCEANIC

V

Technological Revolution in Optics

Communication by photons

Massive optical data storage

Precision laser machining

Medical laser therapy & optical imaging

Blu-ray disc (25GB)CD/DVD

Telephony/data/internet

Laser cutting

Laser writing on human hair Photolithography for manufacture

of computer chips

Corrective laser eye surgery 3-D laser imaging of cell

Optics has an important place in history

Telescope observations forged our understanding of the Universe

Microscopes revealed a micro-universe

Optics, light & vision has been vital for human survival

Today, Optics remains a key

scientific diagnostic technique (e.g.

imaging).

A new revolution in Optics has emerged with the birth of the laser, fibre optics,

integration of optics and electronics, etc..

Particles Waves

Light = EM waves

Historical debate on nature of light

00

1c

or

Wave-particle duality

Quantum OpticsLasers

Planck / EinsteinMichelson Maiman (Laser)…

What is Light? - Revisited

LASER

Paradoxes in physics (BB radiation/ photoelectric effect)Quantisation of light (photons) E=hnBohr model of atomWavefunctions / ProbabilityDiffraction of electrons

Stimulated emission

i

r

Mirror

r=

i

1

2

Refractive index boundary

Snell’s Law n1sin1=n2sin2

n1 n2

Aperture

beam spread

double-slits screen

REFLECTION REFRACTION

DIFFRACTION INTERFERENCE

Fundamentals of Optics

Continuum of waves Finite no. of waves

s s’

O

I

f

F

F’ ho

hI

Imaging Lens

f1

s1

s1

ssm

IMAGING

)cos()sin()cos(

0 tEE

)4/cos(

)cos(

20

ttE

E

a b

L i n e a r p o l a r i s e d E l l i p t i c a l l y p o l a r i s e d

POLARISATION

EM-theory

Safety• Laser Safety

NEVER LOOK DIRECTLY INTO THE LASER OR POINT LASER AT OTHER PERSONS

• Electrical Safety• Trip Hazards

Safety and Lab-book Practices

Your Laboratory Notebook

·        DATE, TIME, TITLE OF EXPERIMENT.

·       CLEAR WRITTEN RECORD AS YOU GO ALONG.

·        DESCRIBE & DRAW WHAT YOU ACTUALLY SEE.

s s’

O

I

f

F

F’

fss111

ssm

Thin lens formula

Magnification formula

PRINCIPLE RAYS: (Any 2 are sufficient to construct image)• Ray passing through the centre of the lens is undeviated.• Ray parallel to the optical axis passes through a focal point.• Ray passing towards, or away from, a focal point emerges

parallel to the axis.

Lenses –Ray Diagrams and Formulae

CONSTRUCTING RAY DIAGRAMS

O object; I images object distance; s’ image distance; f focal length

LENS CALCULATIONS

In later lab-work: you’ll explore issues of real lens (e.g. finite aperture; lens aberration)

• Find a lab-partner & Sit at one of the Optical Set-ups

1. Open your lab-book and write date and time 2. Write heading “Introduction to Experiments in Optics” 3. Write sub-heading: “A. Thin Lens Imaging”

Before we proceed to first experiment…..

Aligning an Optical Bench

s

object

Light source

s’

image, observed on ground-glass screen lens

Observe from behind ground-glass screen

Optical rail

A good rule of optical alignment is to:

• place one item at a time on bench (starting at light source)

• ensure light propagates parallel to bench (rotate post of light source if

necessary)

• optical components are centred (by adjusting post height) and

• optical components are at right-angles to beam path (by rotating post).

s~150mm

Object, L

Light source

s’

ground-glass screen f=100mm Observe from behind ground-glass screen

Optical rail

Expt 1.1 Imaging with a Lens1. Switch on light source (supply

at ~ 5V preset, do not adjust)

2. As object place slide of letter L, in slot-

holder on light source

3. Place f=100mm lens at object distance s=150mm.Measure s with ruler from

object to lens centre

4. Adjust position of ground-glass screen for sharpest image.

Measure s’.

5. Measure a dimension of object (hO)

and corresponding size in image (hI).

Deduce magnification |m|=hI/hO

• Estimate an error for all experimental values measured s, s’, hO, hI.

hO hI

Errors?

s

s

III

OOO

ss

ss

hh

hh

ss|m|

O

I

hh|m|

mmm

Theoretical prediction

mmm

Experimental measurement

2y

2x

z yx.z

yxz

yxz :form ofequation

Calculate the magnification (inc. standard error) for the two methods.

Do they agree / are they consistent given the errors?

Why is s’ >s?

How might you estimate s’?

4 measured quantities

Experiment 1.2 Measuring focal length of lens

f

Pin-hole object

Light source

mirror f=100mm

Figure 3: Simple method for estimating focal length of a positive lens.

1. Use pin-hole slide as object

2. Angle mirror so you can see reflected spot of light on object slide.

(You may not be able to see this until lens is near its focal length position)

3. Measure focal length f by finding the position for minimum

reflected spot sizeIs focal length f=100mm?

B. Wave-Optics : Single-slit Diffraction

Aperture (width a) causes light to

spread

(diffraction)

a

Near-field (z<a2/l) = Fresnel diffraction

(complex mathematical form)

Far-field (z>>a2/l)= Fraunhofer diffraction(simpler mathematical form

=Fourier Transform)

z

Light pattern at any plane z is the sum of secondary wavelets of the unobstructed aperture (including

phases)

z

secondary wavelets

f

diffracting object Lens, f observing

screen

a) b) x

very distant observing screen

~

diffracted rays at angle meet at infinity

parallel rays meet at a point in focal plane

input light

L

x

Figure 4: The far-field diffracted pattern can be visualised in the focal plane of a lens.

Far-field at focal plane of lens

Problem: Far-field z>> a2/lmay not be convenient for lab bench. Solution: Use lens.

fx

DIODE LASER

f

Diffracting object = variable slit

bi-convex lens f=1000mm

observation screen ‘white card’

Expt.2 Visual Observation of Single-Slit Diffraction Pattern

• Note in you lab-book the effect of changing the slit width.• With the central maximum peak of width ~10mm sketch the

diffraction pattern (to scale)

x

1. Replace white light source by Diode Laser

2. Visually observe diffraction pattern of variable slit on white

screen placed at focal length of lens

2

fax

fax

0sinI)x(I

l

l

-10 -5 0 5 10 0.0

0.2

0.4

0.6

0.8

1.0

Distance

Inte

nsity

xm = m(lf/a)

.... 3 ,2 ,1 m

Positions of zeroes

fx

Far-field Single-Slit Diffraction Pattern

Is this what you see?

x

-10 -5 0 5 10

0.01

0.1

1

Distance

Log

Inte

nsity

-10 -5 0 5 10 0.0

0.2

0.4

0.6

0.8

1.0

Distance

Inte

nsity

Logarithmic Response of the Eye

bi-convex lens f=500mm

Photodiode/slit assembly on translation stage

voltmeter

LASER

f diffracting object = single slit slide

Measurement with a Photo-detector

Measurements:1. Measure voltage of central maximum (V0) and first secondary maximum (V1).2. Measure positions of the first minima (X1 and X-1). Hence calculate the slit width

using: X1 – X-1 = 2lf/a

1. Switch on photodiode power

supply and set voltmeter to 200mV

setting

2. Position central maximum of diffraction pattern to coincide with photodiode slit at centre of its translation stage. You may

need to rotate laser and move diffracting slit sideways to achieve this

lf/a lf/a

I0

I1

X1X-1

Final Comments

It is hoped that this introductory Optics session has given you:• some useful practice in laboratory work (inc. lab notebook

and errors)• provided some groundwork for more advanced Optics you

will perform in the lab later in the year.• confidence in working in the UG laboratory