Resolving power and collecting power

Draw a ray diagram for an astronomical telescope in normal adjustment.

Include in your diagram:

three non-axial rays

labelled principal foci for the lenses.

An astronomer has two telescopes A and B.

The astronomer uses each telescope to make observations of Mars when Mars is 0.55 AU from the Earth.

Table 1 gives information about A and B.

angular resolution of the eye ≈ 3 × 10⁻⁴ rad

Compare the images formed by A and B.

In your answer, refer to:

the relative brightness of the images

the ability of each telescope to show features on Mars

the effect of any aberrations caused by each type of telescope.

One advantage of using a CCD with a telescope is that the data can be stored and processed on a computer.

Explain two other advantages of using a CCD rather than the eye when making an observation with a telescope.

A student uses a refracting telescope in normal adjustment to make observations of Jupiter. The telescope has an angular magnification of 75

The eyepiece has a focal length of 22 mm.

Determine the distance between the eyepiece and the objective lens.

When viewed through the telescope, the image of Jupiter subtends an angle

Calculate, in km, the distance between the Earth and Jupiter.

mean radius of Jupiter = 7.0 × 10⁴ km

The student places a cap over one end of the telescope. The cap has a circular hole in its centre. Figure 1 shows the end of the telescope, the objective lens and the cap.

State and explain the effect that the addition of the cap has on the chromatic aberration caused by the lens.

Explain two other effects that the addition of the cap has on the image of Jupiter.

State what is meant by normal adjustment when applied to an astronomical refracting telescope.

Which combination of lenses gives the largest angular magnification when used as

V1031 and WASP-82 are two stars in the constellation Orion. V1031 appears 40 times brighter than WASP-82 when viewed from Earth. The apparent magnitude of V 1031 is 6.0

Calculate the apparent magnitude of WASP-82.

V1031 is just visible to the naked eye of an astronomer when her pupil diameter is 7 mm.

Suggest whether she can observe WASP-82 using a telescope with an objective diameter of 60 mm. Support your answer with a calculation.

CCDs are often connected to telescopes.

Explain two reasons why this improves the ability of astronomers to observe dim stars.

State the defining property of a black hole.

In 2019, astronomers linked several radio telescopes to produce a single telescope called the EHT. The resolution of the EHT is the same as the resolution that a telescope with an aperture equal to the diameter of the Earth could achieve.

Table 2 shows data about the EHT and the Hubble telescope.

Galaxy M87 is 5.3 × 10⁷ light years from Earth. The supermassive black hole at the centre of M87 has a mass 6.5 × 10⁹ times the mass of the Sun.

The radius of the event horizon is R.

The astronomers propose to use either the EHT or the Hubble telescope to observe stars whose distance from the centre of the black hole is less than 1000 R.

Discuss, with calculations, which telescope is more suitable for this observation.

A star is orbiting the black hole in M87. The star is observed in the plane of its orbit. The wavelength of a spectral line observed in the light emitted from the star varies between a maximum and a minimum value.

maximum value observed = 374.96 nm minimum value observed = 373.53 nm

Calculate the orbital speed of the star.

Draw a ray diagram to show how a converging lens can cause spherical aberration.

Draw a labelled ray diagram for an astronomical refracting telescope in normal adjustment.

Show three non-axial rays passing through both lenses. Label the principal foci of the lenses.

The James Lick telescope is an astronomical refracting telescope. When in normal adjustment, the distance between the lenses of the telescope is 17.4 m and the angular magnification is 750

Calculate the focal length of the eyepiece lens.

The James Lick telescope can be used to identify binary stars.

Two techniques are available using this telescope:

• using a processed image from a CCD, and

• direct observation using the naked eye.

Compare the use of a CCD with the use of the naked eye to observe binary stars with this telescope.

Explain what is meant by the Rayleigh criterion.

A telescope uses wavelengths in the range 90 nm to 120 nm.

Explain why this telescope must be located in space.

Go on to discuss one advantage that this telescope has compared to a telescope with the same aperture that uses visible light.

Table 1 shows information about two telescopes.

Each telescope detects radio waves with a wavelength of 21 cm.

Compare the performances of the telescopes in Table 1 when both are used to observe the same faint radio objects.

Draw a ray diagram for a Cassegrain telescope. Your diagram should show the paths of two rays up to the eyepiece lens. The rays should initially be parallel to the principal axis.

A spacecraft passes Pluto at a distance of 12 500 km. The telescope on board has an aperture of diameter 0.21 m and operates at a wavelength of 450 nm.

Discuss whether this telescope is suitable for studying a crater with a diameter of approximately 1 km on Pluto.

The Hubble telescope has an aperture of diameter 2.4 m.

Compare the collecting power of the Hubble telescope with the telescope on the spacecraft in Question 01.2.

An astrophysicist had to decide whether to use a reflecting telescope or a refracting telescope on the spacecraft in Question 01.2.

Discuss which type of telescope to use.

The lenses used in refracting telescopes can cause chromatic aberration.

Complete Figure 1 to show how a lens produces chromatic aberration.

A Cassegrain telescope uses mirrors.

What are the shapes of the primary and secondary mirrors in a Cassegrain

Table 1 contains information about two telescopes, A and B. Each telescope is planned to be the biggest of its type in the world.

Discuss the similarities and differences between optical reflecting telescopes and radio telescopes. Your answer should include references to:

structure

positioning

collecting power.

Go on to discuss which telescope, A or B, will give a more detailed image of an astronomical object that emits both radio waves and visible light.

The Griffith Observatory in Los Angeles includes an astronomical refracting telescope (Griffith telescope) with an objective lens of diameter 305 mm and focal length 5.03 m

Calculate the wavelength of light for which the Griffith telescope has a minimum angular resolution of 1.8 × 10⁻⁶ rad

The Griffith telescope is used to observe two point objects which subtend an angle of 1.8 × 10^–6 rad at the unaided eye.

The typical human eye has a minimum angular resolution of approximately

Calculate the focal length of the eyepiece lens so that an observer can just resolve the two objects when observing them through the Griffith telescope.

The asteroid Apophis has a diameter of 325 m

It has been calculated that, in 2029, its distance of closest approach to the Earth’s

The Griffith telescope may be used to view Apophis using the eyepiece calculated in question 01.2

Deduce whether this telescope is suitable to obtain a detailed view of Apophis. Support your answer with a calculation.

The telescopes are used to view the same object.

Suggest which telescope in Table 1 produces the brighter image. Support your answer with a suitable calculation.

The minimum angular resolution of a telescope can be determined using the Rayleigh criterion.

Explain what is meant by the Rayleigh criterion.

Discuss which of the two telescopes in Table 1 would be better at resolving the images of two objects that are close together.