Lenses and Telescopes

Question 1

Definition of Principal focus (Focal Point)

Answer 1

The point through which all light parallel to the axis of the lens passes through.

Question 2

Definition of Focal length

Answer 2

The distance between the centre of the lens and the focal point.

Question 3

Constructing ray diagrams through converging lenses

Answer 3

• 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

Question 4

Letters in Lens makers formula
1 1 1
— + — = —
u v f

Answer 4

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)

Question 5

Object distance at u > 2f

Answer 5

Diminished, Inverted, Real

Question 6

Object distance at u = 2f

Answer 6

Same as object, Inverted, Real

Question 7

Object distance at f

Answer 7

Magnified, Inverted, Real

Question 8

Object distance at u

Answer 8

Magnified

Question 9

When object distance is at u=f…

Answer 9

…then the image is formed at infinity

Question 10

Angular magnification in normal adjustment =…

Answer 10

… B/a

Question 11

Definition spherical aberration – lens

Answer 11

Where parallel rays at different distances from principal axis are brought to focus at different points (on principal axis).

Question 12

Definition spherical aberration - mirror

Answer 12

Where parallel rays furthest from the principal axis are brought to focus closer to reflector than rays closest to principal axis.

Question 13

How can spherical aberration be prevented in a mirror

Answer 13

Use a parabolic mirror.

Question 14

Diagram of spherical aberration of a mirror (explanation)

Answer 14

Spherical mirror, multiple rays spread out and parallel

Rays further from principal axis are focused to a point closer to mirror.

Question 15

Effect on image of spherical aberration

Answer 15

Image is blurred

Question 16

Definition chromatic aberration

Answer 16

Where different wavelengths are refracted by different amounts resulting in different focal lengths for different wavelengths (colours).

Question 17

Effect on image of chromatic aberration

Answer 17

Images have multicoloured, blurred edges

Question 18

Diagram of chromatic aberration from a lens (explanation)

Answer 18

Blue light (short wavelengths) are focused closer to lens than Red light (longer wavelengths).

Question 19

Resolving power of telescopes

Answer 19

the smallest angular separation that two point objects can still be discerned as separate

Question 20

Definition Rayleigh criteria

Answer 20

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.

Question 21

Definition of Airy Disc

Answer 21

The bright central maximum (spot) of the diffraction pattern produced when light from a point source passes through a circular aperture.

Question 22

Structure and operation of a CCD

Answer 22

• 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.

Question 23

Quantum efficiency of a CCD

Answer 23

Quantum efficiency of pixel >70%

a measure of the proportion of the incident photons that release electrons

Question 24

Definition of quantum efficiency

Answer 24

The percentage of the photons incident on the CCD that release electrons and so are detected

Question 25

Why are telescopes put into space?

Answer 25

• 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

Question 26

(In space) Spitzer - Diameter, spectrum, wavelength, resolution /rad, used for

Answer 26

d=0.85m, Infra red, 5 micrometers, 7x10^-6 rad, observing nebulae

Question 27

(In space) Cos - Diameter, spectrum, wavelength, resolution /rad, used for

Answer 27

d=2.4m, UV, 200 nm, 9x10^-8 rad, analysing quasars

Question 28

(In space) Chandra - Diameter, spectrum, wavelength, resolution /rad, used for

Answer 28

d=1.2m, X-ray, 1 nm, 3x10^-9 rad, discovering super massive black holes

Question 29

(On Earth) Jodrell Bank - Diameter, spectrum, wavelength, resolution /rad, used for

Answer 29

d=76m, Radio, 60 mm, 8x10^-4 rad, discovering distant pulsars

Question 30

(On Earth) UKIRT - Diameter, spectrum, wavelength, resolution /rad, used for

Answer 30

d=3.8m, Radio, 1 micrometer, 7x10^-7 rad, finding exoplanets

Question 31

What does collection power of a telescope depend upon?

Answer 31

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

Question 32

What absorbs X-rays, UV and infra-red in Earth’s atmosphere?

Answer 32

• 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)

Question 33

Similarities and differences between radio and optical telescopes

Answer 33

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

Question 34

Advantages of mirrors in telescopes rather than convex lens

Answer 34

• 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

Question 35

Disadvantages of mirrors in telescopes rather than convex lens

Answer 35

• 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

Question 36

Advantage of larger objective diameter (mirror or lens)

Answer 36

• It collects more light – so can observe fainter objects

* It has a higher resolution – possible to distinguish (resolve) two objects close together.