Optical Telescopes
SPEC 3.9.1.1 & 3.9.1.2 • ASTROPHYSICS
Refracting and reflecting telescope design, ray diagrams, angular magnification, and aberrations
Key Definitions
Before studying telescopes, understand these fundamental concepts:
Converging Lens
A convex lens that focuses parallel incident light to a point (the principal focus).
Principal Focus (F)
The point where rays parallel to the principal axis converge after passing through a converging lens.
Real Image
Formed where light rays actually cross. Can be projected onto a screen.
Virtual Image
Formed where rays appear to come from. Cannot be projected — rays don't actually cross.
Focal Length (f)
The distance from the centre of the lens to the principal focus. Shorter focal length = stronger lens.
Why Use Telescopes?
The main purposes of a telescope used for astronomy are:
Three Main Purposes
To gather as much light as possible — using a large aperture lens or mirror. The amount of light gathered depends on the area of the lens/mirror.
To resolve fine detail — also requires a large aperture. The larger the aperture, the finer the detail that can be seen.
To magnify the image — using a lens or mirror with a long focal length.
Exam Tip
The power of a lens is P = 1/f, where f is the focal length in metres. A short focal length means a more powerful (stronger) lens.
The Refracting Telescope
Refracting telescopes consist of two converging lenses:
Objective Lens
Collects light and creates a real image of a distant object.
Should have a long focal length (fₒ) and be large to collect as much light as possible.
Eyepiece Lens
Magnifies the image produced by the objective lens.
Produces a virtual image at infinity since light rays emerge parallel. This reduces eye strain.
Normal Adjustment
Normal adjustment is when the distance between the objective and eyepiece equals the sum of their focal lengths (fₒ + fₑ). This means the principal focus (F) for both lenses is in the same place.
Ray Diagram: Refracting Telescope
In normal adjustment, the focal points of both lenses coincide:
Key Features
Parallel rays from a distant object converge at the initial image position (focal point). The eye lens produces parallel rays creating a final image at infinity for comfortable viewing.
Angular Magnification
Definition
The angular magnification (M) of a telescope is:
Important
M is always larger angle over smaller angle. When α and β are both less than 10°:
Why fₒ/fₑ Works
For small angles, tan θ ≈ θ (in radians). The objective creates an image of height h at its focal point. From the geometry: β ≈ h/fₒ and α ≈ h/fₑ. Dividing these gives M = fₒ/fₑ. A longer objective and shorter eyepiece give higher magnification.
01Worked Example
Calculate the magnification of a telescope with an objective of focal length 1200 mm using two different eyepieces:
(a) fₑ = 25 mm (b) fₑ = 10 mm
Using M = fₒ/fₑ:
a)
M = 1200/25 = 48×
b)
M = 1200/10 = 120×
Note: A shorter eyepiece focal length gives higher magnification.
Worked Example02
An astronomer requires a telescope with angular magnification of 80× and total length of 810 mm in normal adjustment. Calculate the focal lengths of both lenses.
1
Set up equations: M = fₒ/fₑ = 80, so fₒ = 80fₑ
•
L = fₒ + fₑ = 810 mm
2
Substitute: 80fₑ + fₑ = 810
•
81fₑ = 810, so fₑ = 10 mm
3
Find fₒ: fₒ = 80 × 10 = 800 mm
Reflecting Telescopes
Reflecting telescopes use mirrors instead of lenses. The most common design is the Cassegrain reflecting telescope.
Primary Mirror
Concave parabolic mirror with a long focal length and hole in the centre.
Collects and focuses incoming light.
Secondary Mirror
Small convex mirror positioned in the centre.
Reflects light back through the hole in the primary, making the telescope shorter.
Mirror Construction
Mirrors are a very thin coating (often less than 25 nm thick) of aluminium or silver deposited onto a backing. Curvature is accurate to within λ/8 (one eighth of a wavelength of green light).
Cassegrain Reflecting Telescope
Light Path
Parallel light → reflects from concave primary → converges toward principal focus → intercepted by convex secondary → reflects back through hole → focused by eyepiece lens
Why Use a Convex Secondary?
The convex secondary mirror diverges the converging rays, effectively increasing the focal length of the system without increasing the tube length. This allows a compact design with high magnification. The eyepiece is conveniently located at the back of the telescope, making it easier to mount cameras and other equipment.
Newtonian Reflecting Telescope
An alternative design uses a plane (flat) mirror at 45° instead of a convex secondary:
Cassegrain vs Newtonian
The Cassegrain is shorter because the convex secondary extends the effective focal length. It also allows heavier detection equipment to be mounted at the back.
How the Newtonian Works
The plane mirror at 45° simply redirects the converging light rays to the side of the tube — it does not change the focal length. The eyepiece is mounted on the side of the tube near the top. This design is simpler and cheaper to construct than the Cassegrain, but the observer's head can block incoming light when viewing.
Chromatic Aberration
Definition
Chromatic aberration occurs because blue light is refracted more than red, so different wavelengths focus at different points. This causes an image with coloured fringes.
Effect on Telescopes
Refractors SUFFER from chromatic aberration (light passes through glass).
Reflectors are UNAFFECTED — all wavelengths reflect the same way.
Why Does This Happen?
The refractive index n depends on wavelength. Blue light has a shorter wavelength, so glass has a higher refractive index for blue light. Using n = c/v, higher n means slower speed in glass, causing more bending. This is called dispersion — the same effect that creates rainbows. In telescopes, this produces coloured fringes around bright objects.
Spherical Aberration
Definition
Spherical aberration occurs when rays hitting the edge of a spherical lens/mirror focus at a different position to rays near the centre. This causes image blurring.
Solution
Use parabolic objective mirrors in reflecting telescopes. A parabola brings all parallel rays to a single focus.
Why Does This Happen?
A spherical surface is not the ideal shape for focusing parallel rays. Rays hitting the outer edges of a spherical lens or mirror are bent too much and focus closer to the lens than rays near the centre. This creates a blurred image with no single sharp focus. A parabolic shape has a varying curvature that compensates for this effect, bringing all parallel rays to exactly the same focal point.
Refractors vs Reflectors
Disadvantages of Refracting TelescopesAdvantages of Reflecting Telescopes
Glass must be pure and free from defects throughout.Only the surface needs to be perfect — glass doesn't need to be pure.
Large lenses can bend and distort under their own weight .Mirrors are lighter and easier to handle and manoeuvre.
Lenses can only be supported from the edges (weakest point).Mirrors can be supported from behind .
Chromatic and spherical aberration both affect lenses.No chromatic aberration . Spherical aberration solved with parabolic mirrors.
Large magnifications require very long telescopes.Large composite mirrors can be made from segments.
Important
Chromatic aberration can affect the eyepiece lens in a reflector, but this can be solved using an achromatic doublet.
Worked Example03
A star subtends an angle of 2.0 × 10⁻⁵ rad at the unaided eye. When viewed through a telescope with fₒ = 1.5 m and fₑ = 30 mm, what angle does the image subtend?
1
Convert: fₒ = 1.5 m = 1500 mm, fₑ = 30 mm
2
Magnification: M = fₒ/fₑ = 1500/30 = 50
3
Image angle: α = M × β = 50 × 2.0 × 10⁻⁵
α = 1.0 × 10⁻³ rad (or 1.0 mrad)
Worked Example04
Explain why a Cassegrain reflecting telescope is preferred over a refracting telescope for observing distant galaxies.
1
No chromatic aberration: Mirrors reflect all wavelengths equally, producing sharper images.
2
Larger aperture possible: Mirrors can be supported from behind and made in segments (8-10m diameter). More light collected from faint galaxies.
3
Parabolic mirrors eliminate spherical aberration: All parallel rays focus at the same point.
4
Compact design: Folded light path produces a shorter telescope.
5
Lighter: Mirrors are less heavy than equivalent lenses.
Practice
Question 1: A telescope has an eyepiece of focal length 20 mm. What focal length objective is needed for an angular magnification of 35×?
1
Using M = fₒ/fₑ, rearrange: fₒ = M × fₑ
2
fₒ = 35 × 20 = 700 mm
Practice
Question 2: A refracting telescope in normal adjustment is 660 mm long with magnification 32×. Calculate both focal lengths.
1
From M = fₒ/fₑ = 32: fₒ = 32fₑ
2
From L = fₒ + fₑ = 660: 32fₑ + fₑ = 660
3
33fₑ = 660, so fₑ = 20 mm
4
fₒ = 32 × 20 = 640 mm
Practice
Question 3: Explain how an achromatic doublet reduces chromatic aberration.
1
An achromatic doublet consists of a convex lens (crown glass) cemented to a concave lens (flint glass).
2
The two types of glass have different dispersive properties.
3
The concave flint lens partially cancels the dispersion from the convex crown lens.
4
Different wavelengths focus at approximately the same point, reducing colour fringing.
Summary
Key Formulas
QuantityFormula
Angular magnificationM = α/β = fₒ/fₑ
Telescope length (normal adjustment)L = fₒ + fₑ
Refracting Telescope
Two converging lenses
Objective: long fₒ, collects light
Eyepiece: short fₑ, magnifies
Suffers chromatic + spherical aberration
Reflecting Telescope
Cassegrain: concave primary + convex secondary
No chromatic aberration
Parabolic mirrors fix spherical aberration
Can be larger and lighter
Exam Tip
All the really large telescopes today are reflectors. The largest have mirrors up to 10 m in diameter.
Next: Key Definitions