11.3 DIFFRACTION 11.4 RESOLUTION 11.5 POLARIZATION HW ...

11.3 DIFFRACTION HW/Study Packet
11.4 RESOLUTION
11.5 POLARIZATION

Required: SL/HL
READ Hamper, pp 138-148 Supplemental:
Cutnell and Johnson, pp 842-864
Tsokos, pp 259-278

REMEMBER TO….
 Work through all of the ‘example problems’ in the texts as you are reading them
 Refer to the IB Physics Guide for details on what you need to know about this topic
 Refer to the Study Guides for suggested exercises to do each night
 First try to do these problems using only what is provided to you from the IB Data Booklet
 Refer to the solutions/key ONLY after you have attempted the problems to the best of your ability

UNIT OUTLINE

I. DIFFRACTION OF LIGHT AT A SINGLE SLIT
A. DIFFRACTION REVISITED
B. DIFFRACTION AND INTERFERENCE PATTERNS OF LIGHT
C. THE EQUATION FOR THE FIRST MINIMUM IN THE DIFFRACTION PATTERN

II. THE RAYLEIGH CRITERION
A. WHAT IS MEANS TO BE ‘JUST RESOLVED’
B. THE EQUATION FOR IMAGES TO BE ‘JUST RESOLVED’

III. USES AND APPLICATIONS OF RESOLUTION
IV. POLARIZING FILTERS

A. HOW A POLARIZING FILTER WORKS
B. INTENSITY OF LIGHT AND MALUS’ LAW
C. USING MORE THAN ONE POLARIZING FILTER
V. REFLECTIVE SURFACES
A. HOW REFLECTIVE SURFACES POLARIZE LIGHT
B. BREWSTER’S LAW
C. OPTICALLY ACTIVITY
VI. USES AND APPLICATIONS OF POLARIZATION

FROM THE IB DATA BOOKLET

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WHAT YOU SHOULD BE ABLE TO DO AT THE END OF THIS TOPIC

□ Draw diffraction patterns from a rectangular slits, sharp edges, thin tubes, and circular apertures
□ Be able to identify the first, second, and third single slit diffraction patterns
□ Derive the formula for position of the first minimum in a single slit diffraction pattern
□ Draw intensity patterns for a single slit of finite width and for two slits of negligible width
□ Show the effect of slit width on the intensity pattern of two slits
□ Sketch the variation with angle of diffraction of the relative intensity of light from two point sources

diffracted through a single slit
□ Understand what is meant by resolution and apply the Rayleigh criterion
□ Describe the significance of resolution in CDs, DVDs, electron microscopes, and radio telescopes
□ Explain polarization and how light can be polarized
□ State and apply Malus’s Law and Brewster’s Law
□ Describe optical activity and optically active substances
□ Identify and outline applications of polarized light

HOMEWORK PROBLEMS:

1. A single slit of width 1.50 μm is illuminated with light of wavelength 500.0 nm. Find the angular width

of the central maximum. [38.9°]

2. Microwaves of wavelength 2.80 cm falls on a slit and the central maximum at a distance of 1.0 m from

the slit is found to have a half-width (distance from middle of central fringe to first minimum) is 0.67 m.

Find the width of the slit. [5.0 cm]

3. The intensity pattern for a single-slit diffraction is shown

(vertical units are arbitrary). Find the width of the slit in terms

of the wavelength of light being used. [1.556λ]

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4. Plane wavefronts of monochromatic light
of wavelength λ are incident on a narrow
slit. After passing through the slit they
are incident on a screen placed a large
distance from the slit.

The width of the slit is b and the point X
is at the centre of the slit. The point M on
the screen is the position of the first
minimum of the diffraction pattern
formed on the screen.
The path difference between light from
the top edge of the slit and light from the
bottom edge of the slit is l.

a) Use the diagram to explain why the distance l is equal to λ.

The wavefronts in (a) are from a
monochromatic point source S1. Diagram
1 is a sketch of how the intensity of the
diffraction pattern formed by the single
slit varies with angle θ. The units on the
vertical axis are arbitrary. Another
identical point source S2 is placed close
to S1 as shown in diagram 2. The
diffraction patterns formed by each
source are just resolved.

Diagram 1

Diagram 2
b) On diagram 1 sketch the intensity distribution of the light from source S2.

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c) Outline how the Rayleigh criterion affects the design of radio telescopes.

d) The dish of the Arecibo radio telescope has a diameter of 300 m. Two distant radio sources
are 2.0 × 1012 m apart. The sources are 3.0 × 1016 m from Earth and they emit radio waves
of wavelength 21 cm. Determine whether the radio telescope can resolve these sources.
[θ = 8.5 x 10-4 rad; cannot be resolved]

5. A woman is walking along a straight path, which is at right angles to a telephone line, as shown
in the diagram below. Two birds are perched on the line, 0.40 m apart.

(diagram not to scale)

The diameter of the pupil of the woman’s eye is 2.5 mm and the average wavelength of visible light is

550 nm. Use the Rayleigh criterion to estimate the distance D at which the woman will just be able to

see two separate birds. [1500 m]

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6. A space shuttle orbits at a height of 300 km above the surface of the Earth. It carries two panels

separated by a distance of 24 m. The panels reflect light of wavelength 500 nm towards an observer
on the Earth’s surface. The observer views the panels with a telescope of aperture diameter 85 mm.

The panels act as point sources of light for the observer. Determine whether the images of the panels

formed by the telescope will be resolved. [yes they will]

7. The separation of two objects on the surface of Earth is d. The objects are photographed by a camera

in a spy satellite orbiting Earth. The photographic images of the objects are just resolved. Use the

following data to determine d. [2.4 m]

Wavelength of light emitted by the objects = 500 nm
Distance of satellite above surface of Earth = 4.0 × 105 m
Diameter of camera lens
= 0.10 m

8. Plane-polarized light is incident normally on
a polarizer which is able to rotate in the
plane perpendicular to the light as shown.

In diagram 1, the intensity of the incident

light is 8 W m-2 and the transmitted intensity
of light is 2 W m-2. Diagram 2 shows the

polarizer rotated 90° from the orientation in

diagram 1. What is the new transmitted

intensity? [6 W m-2]

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9. Unpolarized light is shone through two identical polarizers whose axes are parallel.

I [50 %]
Determine the ratio .

I0

10. Unpolarized light is incident on the surface of a
plastic. The angle of incidence is θ. The reflected
light is viewed through an analyser whose
transmission axis is vertical.

The variation with θ of the intensity I of the
transmitted light is shown in the graph below.

a) Explain why there is an angle of incidence, for which the intensity of the transmitted light is zero.
b) Calculate the refractive index of the plastic. [1.19]

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c) Unpolarized light from a source is split, so that there is a
path difference of half a wavelength between the two
beams. A lens brings the light to focus at point P on a
screen. The lens does not introduce any additional path
difference. State and explain whether any light would be
observed at P, in the case in which the polarizers have
their transmission axes
i) parallel. [no light]

ii) at right angles to each other. [light]

11. A ray of light is incident on the surface of a lake. The angle of incidence is φ.

The reflected light is completely polarized horizontally. The refractive index of water is n.

a) On the diagram above draw the refracted ray. [n = tan φ]
b) Use the diagram to deduce the relationship between φ and n.

c) The refractive index of the water is 1.3. Calculate the value of φ. [52° or 0.92 rad]

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