DP IB Physics: HL

Topic Questions

IBPhysics: HLDPTopic Questions9. Wave Phenomena (HL only)9.4 Resolution

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First teaching 2014

Last exams 2024

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9.4 Resolution

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1
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Which statement is not true about circular apertures?

  • Circular apertures allow a cone of light to enter a region behind the aperture

  • Circular apertures allow light to act like a point source

  • The diffraction of light through a circular aperture produces a diffuse disc surrounded by fainter concentric circular rings

  • The diffraction pattern produced by circular apertures produces a central linear fringe with subsequent alternating dark and light fringes

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2
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What does the Rayleigh criterion describe?

  • The diffraction of light through a single slit

  • The diffraction of light through a double slit

  • The diffraction of light through multiple slits

  • The minimum separation between two light sources that can be resolved into two distinct objects

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3
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The diagram below shows the light from two point sources, s1 and s2 passing through a circular aperture.

cfSbxKUZ_9-4-ib-hl-emcq-3-q-stem

What name is given to the angle shown as θ?

  • Angular separation

  • Angle of diffraction

  • Angle of incidence

  • Angle of reflection

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4
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Light from two sources with wavelength λ is passed through a circular aperture with diameter b, producing an angle of diffraction θ.

According to the Rayleigh criterion, how would the angle of diffraction be affected if the diameter of the aperture was doubled?

  • 0.25 space theta

  • 0.50 space theta

  • theta

  • 2 space theta

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5
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Which of the following options would not increase the resolution of two objects?

  • Decreasing the wavelength of the light

  • Increasing the angular separation of the objects

  • Increasing the diameter of the aperture

  • Increasing the angle of diffraction

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6
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The Rayleigh criterion can be presented as:

 s over d space greater or equal than space 1.22 lambda over b

Which option provides the correct quantities represented in the expression?

 

 

s

d

λ

b

A.

Distance between sources

Distance between source and aperture

Wavelength

Diameter of aperture

B.

Distance between source and aperture

Distance between sources

Wavelength

Diameter of aperture

C.

 Wavelength Diameter of aperture

Distance between sources

 		 Distance between source and aperture

D.

 Diameter of aperture

Wavelength

Distance between source and aperture

Distance between sources

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7
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The Rayleigh criterion can also be applied to diffraction gratings. 

Incident light with an average wavelength of 600 nm is incident on a diffraction grating. The difference between the wavelengths is 25 nm. How may slits would the grating need to have to resolve fully the second order of diffraction?

  • 24

  • 25

  • 12

  • 50

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8
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Which of the following objects can be resolved according to the Rayleigh criterion?

9-4-ib-easy-mcq-q8

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9
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The Rayleigh criterion can be expressed as:

 s over d space greater or equal than space 1.22 lambda over b

A telescope is aimed at two objects that are known to be 10 cm apart. The angle of diffraction is 4.5 × 10−5 rad.

Can the objects be resolved at a distance of 10 km?

  • Yes, because 1 cross times 10 to the power of negative 5 end exponent space greater than space 4.5 cross times 10 to the power of negative 5 end exponent

  • No, because 1 cross times 10 to the power of negative 5 end exponent space less than space 4.5 cross times 10 to the power of negative 5 end exponent

  • Yes, because 1 cross times 10 to the power of negative 3 end exponent space greater than space 4.5 cross times 10 to the power of negative 5 to the power of blank end exponent

  • No, because 1 cross times 10 to the power of negative 3 end exponent space less than space 4.5 cross times 10 to the power of negative 5 end exponent

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10
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It is not possible to view an object smaller than the wavelength used to see it. 

Which of the following can be used to resolve objects smaller than the wavelengths of visible light, such as atoms?

  • Sodium ions

  • Electrons

  • Gold atoms

  • Water molecules

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1
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A driver with normal eyesight sees a vehicle approaching in the distance with its headlights on. The road is long and straight, and the sun has just set behind the driver. The driver cannot tell if the approaching vehicle is a car or a motorbike. 

What is a fair estimation of the maximum distance between the approaching vehicle and the driver at which the object will become clear?

  • 6 km

  • 8 km

  • 10 km

  • 12 km

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2
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The Jodrell Bank radio telescope is used to form images of astronomical objects. However, the telescope's resolving power is less than that of the human eye. 

What is a fair estimation of the difference in the resolving power between the Jodrell Bank telescope and the human eye given to the nearest order of magnitude?

  • 10 to the power of 1

  • 10 squared

  • 10 cubed

  • 10 to the power of 4

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3
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The Arecibo radio telescope has a diameter of 300 m and detects wavelengths of approximately 8 cm. Astronomers can use it to view the Andromeda galaxy at a distance of 3 × 106 light years from Earth. The Andromeda galaxy has a diameter of 2 × 105 light years. Which is the most likely description of the image of the andromeda galaxy as seen by the astronomers.

  • A single point source

  • A single circular smudge

  • An oval smudge

  • A resolved image

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4
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The Hubble space telescope has a mirror of diameter 2 m and works with cameras that operate with wavelengths between 100 nm - 1000 nm. It can be pointed at a distant star with an accuracy of of about 4 × 10−8 rad.

What is the theoretical limit of resolution using each of the wavelengths quoted?

 

 

λ = 100 nm

λ = 1000 nm

A.

6.1 × 10−6 rad

6.1 × 10−5 rad

B.

1.0 × 10−7 rad

5.7 × 10−7 rad

C.

 3.4 × 10−5 rad

4.5 × 10−8 rad

D.

 2.1 × 10−8 rad

6.5 × 10−7 rad

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5
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The ability of a telescope to resolve two closely spaced objects is called its resolving power. The diagram below shows two different structures of telescope.

i-phctlt-9-4-ib-hl-hmcq-5-q-stem

Which structure of telescope has the greatest resolving power?

  • The single paraboloid

  • The array of parabolic dishes containing nine dishes

  • The array of parabolic dishes containing twelve dishes

  • The resolving power of all the structures is the same

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Images like the one below can be used to determine to what extent the human eye can resolve different frequencies of light. 

tsm0QTqN_9-4-ib-hl-hmcq-6-resolving-power-of-eye

The human eye can detect wavelength between 740 nm and 380 nm represented by the 44 colours in the diagram. 

What is the resolving power of the human eye at the following colours?

 

 

Red 

λ = 740-625 nm

Orange

λ = 625-590 nm

Yellow

λ = 590-565 nm

Green

λ = 565-520 nm

A.

85

72

76

68

B.

68

85

72

76

C.

 68 72 85 85

D.

 85

76

72

68

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7
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The Hale telescope uses a diffraction grating to resolve objects. A diffraction grating of 10 cm is used containing 200 lines per mm. Assuming the wavelength of incident light to to be 5 μm, what is the resolving power of the telescope?

  • R space equals space 5 cross times 10 to the power of 7

  • R space equals space 2 cross times 10 to the power of 4

  • R space equals space 1 cross times 10 to the power of 6

  • R space equals space 5 cross times 10 to the power of 6

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8
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A binary star system containing star X and star Y are viewed from Earth and are known to be 5 light years from Earth and 20 AU from one another. What is a fair estimate of the angular separation of the two stars as seen from Earth?

  • 6 cross times 10 to the power of negative 5 end exponent rad

  • 6 cross times 10 to the power of negative 4 end exponent rad

  • 6 cross times 10 to the power of negative 3 end exponent rad

  • 6 cross times 10 to the power of negative 2 end exponent rad

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9
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On a sunny day, a person stands on a beach looking at two mountains on the horizon.

A person of average height can see approximately 5 km before the curvature of the Earth removes objects from view.

What is a reliable estimate of the minimum distance between the mountains?

  • 1.3 m

  • 1.8 m

  • 2.3 m

  • 2.8 m

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10
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The centre of the galaxy S5742-b is 2 × 1010 light years away from the Earth. The black hole at its centre has a mass of 9 × 1050 kg. Its two brightest stars are located on opposite sides of the black hole as viewed from Earth and astronomers are hoping to observe the moment that the stars are pulled in. The Effelsberg 100 m radio telescope is one of several being used to monitor the galaxy. It detects radio waves of wavelengths of approximately 1 m.

The radius of a black hole is given by: 

 R subscript s space equals space fraction numerator 2 G M over denominator c squared end fraction

Which is the most likely image that the Effelsberg telescope is most likely to resolve?

 

UdCe9w-v_9-4-ib-hl-hmcq-10-ans-options

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1
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An object to be viewed by a microscope is irradiated with red light. 

Which of the following changes would enable two features on the microscope slide to be resolved more clearly?

  • Use blue light

  • Decrease the diameter of the lens

  • Decrease the distance between the microscope lens and the object

  • Change the lens material without changing the refractive index

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2
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An astronomical telescope has a circular collecting dish of diameter 30 cm. It is used to observe two stars that are both emitting electromagnetic radiation of wavelength 3 mm. The images of the stars are just resolved by the telescope.

What angle is subtended by the galaxies at the telescope?

  • 0.01 rad

  • 0.122 rad

  • 0.0122 rad

  • 0.008 rad

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3
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Two car headlights of wavelength λ, have an angular separation of θ, as measured by a person standing a distance d from the car. The radius of the person's pupils is given by r.

Which of the following conditions must be satisfied for the two headlights to be resolved by the person?

  • theta greater or equal than 1.22 lambda over r

  • theta greater or equal than 1.22 lambda over r squared

  • theta greater or equal than 0.61 lambda over r

  • theta less or equal than 1.22 fraction numerator lambda over denominator 2 r end fraction

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4
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Two galaxies emitting light of wavelength 500 nm are observed through a telescope to have angular separation of 1 × 10−6 rad.

The telescope can just resolve the images of the two galaxies. What is the diameter of the telescope's circular collecting dish?

  • 0.61 mm

  • 0.61 m

  • 0.61 × 10−6 m

  • 0.61 cm

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5
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A diffraction grating can be used to resolve two emission wavelengths from an element in the 2nd order of the spectrum. The wavelengths for a certain element are 400 nm and 500 nm.

How many slits on the diffraction grating are illuminated by the beam?

  • 2.25 lines

  • 9.0 lines

  • 0.25 lines

  • 4.5 lines

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6
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Two blue laser beams of identical wavelength pass through a circular aperture. The images of the two sources just fail to be resolved by an observer.

Which change allows for resolution of the images?

  • Moving the two lasers further from the aperture

  • Using red light

  • Decreasing the size of the aperture

  • Replacing the circular aperture with a narrow slit

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7
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A person stands on a cliff at in sunlight with an average wavelength of 600 nm and can just resolve two bushes located on an island in the distance. The distance from the cliff to the island is 2 km. The diameter of the person's pupils is 2.0 mm.

What is the separation of the two bushes?

  • 3.66 × 10−4 m

  • 7.32 × 10−4 m

  • 0.732 m

  • 366 m

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8
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A diffraction grating with 100 lines per mm is used to just resolve two wavelengths of light in the third order spectrum. The beam of light has a width of 0.2 mm. The average of the two wavelengths is 600 nm. 

What are the values of two wavelengths of light?

  • 590 nm and 610 nm

  • 585 nm and 615 nm

  • 595 nm and 605 nm

  • 570 nm and 630 nm

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9
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Which one of the following combinations of beam width, W and number of lines per mm, L will give maximum resolvance?

 

W / mm

L / mm−1

A.

3.0

200

B.

4.0

100

C.

1.0

350

D.

1.5

500

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10
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A car with two headlights approaches a stationary observer. The light passes through their circular pupils. Under what conditions would the resolution of the two headlights be better?

 

Pupil diameter

Frequency of headlights

A.

 increased increased

B.

 increased decreased

C.

 decreased increased

D.

 decreased decreased

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