Lenses and Optical Telescopes

Question 1

Explain the shape of:

i) biconvex lens
ii) piano-convex lens
iii) piano-concave lens
iv) biconcave lens

Answer 1

i) 2 curved sides where the thickest area is through the principle axis
ii) 1 curved side and a flat side where the thickest area is through the principle axis
iii) 1 curved side and a flat side where the thinnest area is through the principle axis
iv) 2 curved lines where the thinnest area is through the principle axis

Question 2

Describe the axis of symmetry called?

Answer 2

The principle axis

Question 3

Define the principle focus

Answer 3

The point on the principle axis where rays cross which were originally parallel to the principle axis

Question 4

What is the distance between the centre of the lens and the principle focus called?

Answer 4

The focal length

Question 5

Name the 6 types of converging lens

Answer 5

1) biconvex
2) pianoconvex
3) positive meniscus
4) negative meniscus
5) pianoconcave
6) biconcave

Question 6

Describe the image for an object that is beyond 2F

Answer 6

Real
Inverted
Diminished

Question 7

Describe the image for an object that is at 2F

Answer 7

Real
Inverted
Same size

Question 8

Describe the image for an object that is between F and 2F

Answer 8

Real
Inverted
Magnified

Question 9

Describe the image for an object that is between F and the lens

Answer 9

Virtual
Upright
Magnified

Question 10

State the lens formula and state the rules about the signs for focal length and the nature of the image

Answer 10

1 / f = 1 / u + 1 / v
where u is distance from object to lens, and v is from lens to image
- Converging lenses have +ve focal lengths, diverging lenses have -ve focal lenghts
- Distances to real images are +ve, and to virtual images are -ve

Question 11

Define angular magnification and give its units

Answer 11

The ratio of the angle subtended at the eye by the image formed by an optical instrument to that subtended at the eye by the object when not viewed through the instrument.
M = Angle subtended by image of eye (α) / angle subtended by object of unaided eye (β)
Units: Radians (rad)

Question 12

Describe the ray diagram for an astronomical telescope consisting of two converging lenses

Answer 12

The telescope is in normal adjustment because the image is formed at infinity (i.e. light rays leave the telescope parallel)
The focal points of the two lenses coincide, making the distance between them equal to the sum of the focal points

Question 13

Give the equation and units for the angle subtended by an object of height h, distance d away

Answer 13

θ = h /d

units: radians

Question 14

Give the equation relating the focal lengths of the objective and eyepiece lenses to the angular magnification

Answer 14

M = fₒ / fₑ

Question 15

Describe and explain the shape of reflecting telescopes

Answer 15

A parabolic mirror is used to create one focal point, to prevent spherical aberration

Question 16

Define Cassegrain telescope

Answer 16

A reflecting telescope in which light reflected from a convex secondary mirror passes through a hole in the primary mirror.
The focal point is at the hole in the primary mirror and an eye piece is used to make the rays from the secondary mirror parallel

Question 17

Define Newtonian telescope

Answer 17

A reflecting telescope in which the light from the main mirror is deflected by a small flat secondary mirror set at 45°, sending it to a magnifying eyepiece in the side of the telescope.

Question 18

State why reflective telescopes can be larger than refractor telescopes

Answer 18

Because a mirror can be supported from behind, where as a lens must be supported at the edge. Therefore a large lens is likely to break under its own weight

Question 19

State 2 reasons why the size of the telescopes is important

Answer 19

• A larger objective lens means a much greater collecting area (it is proportional to diameter²), meaning fainter objects can be seen
• The larger the diameter of the aperture, the greater the resolving power (the image will show more detail)

Question 20

State 2 reasons why reflecting telescopes are often preferred over refracting telescopes

Answer 20

• Reflectors can be made larger

- Mirrors don’t refract light, therefore don’t suffer from chromatic aberration

Question 21

Define chromatic aberration

Answer 21

The effect produced by the refraction of different wavelengths of light through slightly different angles, resulting in a failure to focus.

Question 22

State and explain 2 common problems with reflecting telescopes

Answer 22

• The secondary mirror and the ‘spider’ holding it in place both diffract the light as it passes, leading to poorer quality images
• There is some refraction eventually in the eyepiece used to view the final image

Question 23

Describe the diffraction pattern produced by a circular aperture

Answer 23

A central maxima surrounded by light and dark rings

Question 24

Give the equation for the angle of the minima for a single slit diffraction pattern

Answer 24

sinθ = nλ / a

where a is the slit width and n is the order of the minima

Question 25

Define Rayleigh Criterion

Answer 25

Two objects will be just resolved if the centre of the diffraction pattern of one image coincides with the first minimum of the order

Question 26

Give the equation for the angular separation for 2 objects that are just resolved and an assumption made for this equation

Answer 26

θ ≈ λ / D
θ = 1.22 λ / D
where θ is in radians, and D is the diameter of the objective
The aperture of the telescope is assumed to be the same as the diameter of the objective

Question 27

Define resolving power

Answer 27

The ability of an optical instrument to separate or distinguish small or closely adjacent images.
The better the resolution, the smaller the angle θ

Question 28

Define CCD

Answer 28

A charge-coupled device (CCD) is a light-sensitive integrated circuit that stores and displays the data for an image in such a way that each pixel (picture element) in the image is converted into an electical charge the intensity of which is related to a color in the color spectrum.

Question 29

Describe the structure of a CCD and how it works

Answer 29

• A silicon chip divided into picture elements (pixels)
• Incident photons cause electrons trapped in ‘potential wells’ to be released
• The number of electrons liberated is proportional to the intensity of light
• When exposure is complete, the charge is processed to give an image
• Quantum efficiency of pixel > 70%