#9 Astrophysics

What is the purpose of a convex lens?

It focuses incident light

What is a convex lens also known as?

A converging lens

What is the purpose of a concave lens?

It spreads out light

What is a concave lens also known as?

A diverging lens

What is the principal axis?

The line passing through the centre of the lens perpendicular to its surface

What is the principle focus of a converging lens?

The point where incident beans passing parallel to the principal axis will converge

What is the principle focus of a diverging lens?

The point from which light rays appear to come from before passing through the lens

Define focal length.

The distance between the centre of a lens and the principle focus

What is the relationship between focal length and lens strength?

The shorter the focal length, the stronger the lens

Explain the difference between a real and a virtual image.

A real image is formed when light rays cross after refraction, and therefore can be formed on a screen

A virtual image is formed on the same side of the lens as the rays approach, so they do not cross and the image cannot be formed on a screen

State the lens formula.

1/(distance from object) + 1/(distance from image) = 1/(focal length)

Define lens power?

A measure of how closely a lens can focus a beam parallel to the principal axis

How does the lens power value differ between converging and diverging lenses?

Converging = positive

Diverging = negative

What is lens power measured in?

Dioptres (D)

What is a refracting telescope made up of?

2 converging lenses (objective and eyepiece)

Give the properties of an objective lens in a refracting telescope.

It collects light to create a real image

Has a long focal length

Large to collect as much light as possible

Give the properties of an eyepiece lens in a refracting telescope.

Magnifies the image produced by the objective lens

Produces a virtual image at infinity

Reduces eye strain so the observes doesn’t have to refocus

What is the normal adjustment for a refracting telescope?

The point where the distance between the objective and eyepiece lens is the sum of their focal lengths

What is important about the principal focuses at normal adjustment?

The principal focus of both lenses is in the same place

Draw a ray diagram for a refracting telescope at normal adjustment.

Give the 2 equations for the magnifying power (M) of a telescope?

M = angle subtended by the image/ angle subtended by the object = f_o/f_e

Describe how a cassegrain telescope is arranged.

A concave primary mirror with a long focal length and a small convex secondary mirror in the centre

Draw a ray diagram for a cassegrain telescope.

How is distortion minimised in a reflecting telescope?

Using very thin (<25nm) aluminium and silver atoms, making it as smooth as possible

What is chromatic aberration?

Different wavelengths (colours) of light are refracted different amounts, so are focused at different points

How might an image appear through a lens when chromatic aberration occurs?

With different colours around the edges

Why does chromatic aberration have very little effect on reflecting telescopes?

It only has one small lens

What is spherical aberration?

When the curvature of a lens/mirror causes light rays at the edges to be focused in different points

What are the consequences of spherical aberration?

A blurred or distorted image

How can spherical aberration be avoided in reflecting telescopes?

Using parabolic objective mirrors

What is an achromatic doublet?

A convex lens made of crown glass and a concave lens made of flint glass cemented together

What is the purpose of an achromatic doublet?

It reduces spherical AND chromatic aberration by focusing the rays in the same position

Draw a diagram of an achromatic doublet.

List the disadvantages of refracting telescopes.

Large lenses can bend/distort under their own weight (very heavy)

Chromatic and spherical aberration affect the lenses

They are very heavy and difficult to manoeuvre

They require long focal lengths and large lenses

They can only be supported at the edges

List the advantages of reflecting telescopes.

Mirrors are very thin and give excellent image quality

Mirrors are unaffected by chromatic aberration and spherical aberration can be reduced using parabolic mirrors

Mirrors are light and can be moved easily

Large mirrors can be made that are easy to support from behind to minimise distortion

Why are radio telescopes able to be used at ground level?

Most radio waves are not absorbed by the atmosphere

Why should radio telescopes be built in isolated areas?

To minimise interference from other sources of radio waves

Draw a diagram of a radio telescope.

Give some similarities between radio and optical telescopes.

Both types focus incident radiation to detect its intensity

Both can be moved to focus on different sources

Parabolic dish is similar to objective mirror in reflecting telescope

Both are ground based

Give some differences between radio and optical telescopes.

Radio wavelengths are larger than visible light, so radio telescopes have a much greater diameter

Radio telescopes are easier and cheaper to construct (wire mesh used)

Radio telescopes experience man-made interference, whereas optical interference is often natural

What is an IR telescope made up of?

2 large concave mirrors that focus radiation onto a detector

Why must IR telescopes be cooled using cryogenic liquids?

To prevent interference from its own components

Why must IR telescopes be shielded?

To avoid thermal contamination from other objects

Why must IR telescopes be launched into space to work?

Earth’s atmosphere absorbs IR radiation

What regions of space are viewed using an IR telescope?

Cooler regions

Why do UV telescopes need to be positioned in space?

The ozone layer absorbs radiation with a wavelength <300nm

What are UV telescopes used to view?

Interstellar medium and star formation regions (hotter regions)

Why do X-ray telescopes need to be positioned in space?

All X-rays are absorbed by the atmosphere

Why must X-ray telescopes use a combination of parabolic and hyperbolic mirrors?

X-rays have so much energy that they would pass through a normal mirror

What is the purpose of a CCD?

To convert EM rays into electrical pulses

What can be observed using X-ray telescopes?

Active galaxies, black holes and neutron stars

What is collecting power?

A measure of a lens or mirror’s ability to collect incident EM radiation

State the relationship between collecting power and diameter of the objective lens.

Collecting power is directly proportional to D²

What is improved by a greater collecting power?

The brightness of the image

What is resolving power?

The ability of a telescope to separate images of close-together objects

Give the equation for minimum angular resolution.

MAR = wavelength / diameter

What is the Rayleigh Criterion?

2 objects will NOT be resolved if any part of the central maximum of either image falls within the first minimum of the other

What is a CCD?

A charge-coupled device

An array of light sensitive pixels that become charged when exposed to light by the photoelectric effect

What is quantum efficiency?

The percentage of incident photons that cause an electron to be released

What is a spectral range?

The detectable range of wavelengths of light

What is pixel resolution?

The number of pixels used to form an image on the screen

What is spatial resolution?

The min distance apart objects must be to be distinguishable

Compare the CCD and human eye based on quantum efficiency, resolution and convenience.

The CCD has a quantum efficiency of ~80%, compared to 4-5% of the eye

The CCD can detect IR, UV and visible light

CCD has a better pixel and spatial resolution

a CCD is less convenient as it must be set up

Define luminosity.

The power output of a star (energy released per second)

What is the intensity of a star?

The luminosity per unit area

How does the intensity of a star change with distance?

Intensity is inversely proportional to the square of the distance from the star

What is the apparent magnitude of a star?

How bright it appears in the sky

What is the Hipparcos scale?

A classification system for stars depending on their apparent magnitude

How is the Hipparcos scale read?

1 is the brightest, 6 is the faintest

How bright is a magnitude 1 star compared to a magnitude 6 star?

100 times brighter

What is the difference in intensity of a star for a difference of 1 on the Hipparcos scale?

2.51x

What is absolute magnitude?

The apparent magnitude of a star if it were 10 parsecs from earth

Give the equation relating the apparent (m) and absolute magnitude (M) of a star.

m - M = 5log(d/10)

What is parallax?

The apparent change of a position of a nearer star in comparison to distant stars in the background as a result of the orbit of the earth around the sun

How does angle of parallax relate to the distance from earth?

Larger angle = closer to earth

Define the astronomical unit (AU) and give its value.

The average distance from the centre of the earth to the centre of the sun

1AU = 1.5 × 10¹¹ m

What is a parsec?

The distance at which the angle of parallax is 1 arcsecond

What is the value in m of one parsec?

3.08 × 10¹⁶ m

What is a light year?

The distance that an EM waves travels in a vacuum in a year

How many m in a light year?

9.46 × 10¹⁵ m

How can parallax angle be used to find the distance to a star?

distance (in parsecs) = 1/parallax angle (in arcseconds)

What is a black-body radiator?

A perfect emitter and absorber of all possible wavelengths of radiation

State Stefan’s law.

The luminosity of a black-body radiator is directly proportional to its A (surface area) and T⁴

Give the value of the Stefan constant.

5.67 × 10^-8

State the equation for Stefan’s law.

P = (constant) x A X T⁴

State Wien’s displacement law.

The peak wavelength of emitted radiation is inversely proportional to the absolute temperature of the object

What is the peak wavelength of a source?

The wavelength released at maximum intensity

State the equation for Wein’s law.

peak wavelength x T = 2.9 × 10^-3 mK (metres kelvin)

What happens to the peak wavelength of a body as it gets hotter?

It decreases

What assumption is made when applying Wein’s law?

Light is emitted equally in all directions

Give an equation relating the intensity, power output and distance of a star from earth.

I = P/4pi(d²)

What are spectral classes dependent on?

The strength of absorption lines on a spectrum and therefore the temperature of the star

What are hydrogen-balmer lines?

Absorption lines that are found in spectra of O,B and A type stars

What causes hydrogen-balmer lines?

The excitation of hydrogen atoms from the n=2 state to higher/lower energy levels

Why do cooler stars not have hydrogen-balmer lines?

The hydrogen atoms do not become excited, or may not be present at all

Give the colour, temperature and prominent absorption lines of a class O star.

Blue

25,000 - 50,000 K

He⁺, He, H

Give the colour, temperature and prominent absorption lines of a class B star.

Blue

11,000 - 25,000 K

He, H

Give the colour, temperature and prominent absorption lines of a class A star.

Blue/White

7,500 - 11,000 K

H, ionised metals

Give the colour, temperature and prominent absorption lines of a class F star.

White

6000 - 7500 K

Ionised metals

Give the colour, temperature and prominent absorption lines of a class G star.

Yellow/White

5000 - 6000 K

Ionised and neutral metals