Lenses and Telescopes Flashcards
Definition of Principal focus (Focal Point)
The point through which all light parallel to the axis of the lens passes through.
Definition of Focal length
The distance between the centre of the lens and the focal point.
Constructing ray diagrams through converging lenses
- One line is drawn parallel to the principal axis of the lens through to the centre line of the lens, where it then bends and passes through the focal point (principal focus).
- One line is drawn through the centre of the lens.
- The top of the image is formed where the two construction rays cross.
Remember to mark the principal focus on both sides of lens
Letters in Lens makers formula
1 1 1
— + — = —
u v f
u is the Object distance
v is the Image distance
f is the focal length of lens
u comes before v in the alphabet, object comes before image in lens
RIP – Real Is Positive
(Real image has positive distance, Virtual image has negative distance)
Object distance at u > 2f
Diminished, Inverted, Real
Object distance at u = 2f
Same as object, Inverted, Real
Object distance at f
Magnified, Inverted, Real
Object distance at u
Magnified
When object distance is at u=f…
…then the image is formed at infinity
Angular magnification in normal adjustment =…
… B/a
Definition spherical aberration – lens
Where parallel rays at different distances from principal axis are brought to focus at different points (on principal axis).
Definition spherical aberration - mirror
Where parallel rays furthest from the principal axis are brought to focus closer to reflector than rays closest to principal axis.
How can spherical aberration be prevented in a mirror
Use a parabolic mirror.
Diagram of spherical aberration of a mirror (explanation)
Spherical mirror, multiple rays spread out and parallel
Rays further from principal axis are focused to a point closer to mirror.
Effect on image of spherical aberration
Image is blurred
Definition chromatic aberration
Where different wavelengths are refracted by different amounts resulting in different focal lengths for different wavelengths (colours).
Effect on image of chromatic aberration
Images have multicoloured, blurred edges
Diagram of chromatic aberration from a lens (explanation)
Blue light (short wavelengths) are focused closer to lens than Red light (longer wavelengths).
Resolving power of telescopes
the smallest angular separation that two point objects can still be discerned as separate
Definition Rayleigh criteria
two point objects can be just be resolved when the central maximum of the diffraction pattern of one object lies over the first minimum of the diffraction pattern of the other.
Definition of Airy Disc
The bright central maximum (spot) of the diffraction pattern produced when light from a point source passes through a circular aperture.
Structure and operation of a CCD
- A CCD is silicon chip divided into picture elements (pixels).
- Incident photons cause electrons to be released.
- The number of electrons liberated is proportional to the intensity of the light.
- These electrons are trapped in ‘potential wells’ in the CCD.
- An electron pattern is built up which is identical to the image formed on the CCD.
- When exposure is complete, the charge is processed to give an image.
Quantum efficiency of a CCD
Quantum efficiency of pixel >70%
a measure of the proportion of the incident photons that release electrons
Definition of quantum efficiency
The percentage of the photons incident on the CCD that release electrons and so are detected
Why are telescopes put into space?
- Electromagnetic waves are absorbed by the atmosphere
- Light pollution and other interference at ground level
- The effect the atmosphere has on the path of the light as it passes through
(In space) Spitzer - Diameter, spectrum, wavelength, resolution /rad, used for
d=0.85m, Infra red, 5 micrometers, 7x10^-6 rad, observing nebulae
(In space) Cos - Diameter, spectrum, wavelength, resolution /rad, used for
d=2.4m, UV, 200 nm, 9x10^-8 rad, analysing quasars
(In space) Chandra - Diameter, spectrum, wavelength, resolution /rad, used for
d=1.2m, X-ray, 1 nm, 3x10^-9 rad, discovering super massive black holes
(On Earth) Jodrell Bank - Diameter, spectrum, wavelength, resolution /rad, used for
d=76m, Radio, 60 mm, 8x10^-4 rad, discovering distant pulsars
(On Earth) UKIRT - Diameter, spectrum, wavelength, resolution /rad, used for
d=3.8m, Radio, 1 micrometer, 7x10^-7 rad, finding exoplanets
What does collection power of a telescope depend upon?
Collection power of a telescope (rate at which energy is collected) is proportional to the cross-sectional area of the objective (lens or mirror).
Collecting power of a telescope is proportional to d^2
What absorbs X-rays, UV and infra-red in Earth’s atmosphere?
- X-rays are absorbed by Ozone (and Oxygen)
- UV are absorbed by Ozone (and Oxygen)
- Infra-red are absorbed by water vapour (and carbon-dioxide)
Similarities and differences between radio and optical telescopes
Similarities
• Radio telescopes have a similar structure in that a concave reflecting surface reflects electromagnetic radiation to a detector at the focal point (of the reflecting surface).
Differences
• Radio telescopes are much larger – radio wavelengths are much longer than optical wavelengths
• Radio telescopes have a lower resolving power – the wavelengths of radio waves are very much larger than optical wavelengths (even though the diameters of radio telescopes are larger).
• Radio telescopes have a greater collecting power – collecting power depends on the area of the objective which is much larger for radio telescopes (depends on the square of the diameter).
• Radio telescopes are not as affected by atmosphere so their positioning is less critical
• Radio telescopes have only 1 reflecting surface not 2
Advantages of mirrors in telescopes rather than convex lens
- No chromatic aberration – mirrors do not refract light
- no spherical aberration – use of parabolic mirror
- no distortion – mirrors can be supported across its whole surface (lenses can only be supported around their edge)
- better resolving power and/or greater brightness – mirrors can be made larger
- more light gets through (image is brighter) – lens absorbs more light
Disadvantages of mirrors in telescopes rather than convex lens
• they have a frame holding the central mirror (secondary), that:
o reduces the light intensity (as it blocks some light from hitting the primary mirror)
o creates diffraction effects around the edges causing blurring of the image
Advantage of larger objective diameter (mirror or lens)
- It collects more light – so can observe fainter objects
* It has a higher resolution – possible to distinguish (resolve) two objects close together.
