Resolution (DP IB Physics: HL)

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?

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?

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?

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?

A diffraction grating can be used to resolve two emission wavelengths from an element in the 2^nd 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?

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?

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?

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?

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

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?

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?

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?

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.

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?

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.

Which structure of telescope has the greatest resolving power?

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

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?

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?

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?

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?

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: 

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