SME
Grade 12 Science · Problem type
A telescope’s magnification and light-gathering
Use this for “A telescope has a 900 mm objective and a 25 mm eyepiece. What is its magnification?”
Diagram
M = fₒ/fₑ = 900/25 = 36
The lenses are fₒ + fₑ = 925 mm apart; the objective’s focus is the eyepiece’s.
A bigger objective gathers more light; its focal length over the eyepiece’s sets the magnification.
This is an example. Type your own values to start a new problem.
M
=
fₒ (mm)
÷
fₑ (mm)
L
Tube length
worked out (not typed)
D
Aperture
example
G
Times more light than the eye
worked out (not typed)
Formulas
M
=
fₒ
fₑ
36
=
900
25
L
=
fₒ
+
fₑ
925 = 900 + 25
G
=
(
D
7
)
2
204
=
(
100
7
)
2
Assumptions
•
Aperture, not magnification, sets how faint a star you can see.
•
Mirrors can be made far larger than lenses.
•
The eye’s pupil opens to about 7 mm in the dark.
Step-by-step
WE KNOW
fₒ = 900 mm, fₑ = 25 mm, D = 100 mm
FIND
magnification (M), tube length (L), times more light than the eye (G)
Step 1 · Find magnification (M)
Use M = fₒ ÷ fₑ
The objective’s focal length over the eyepiece’s.
M
=
900
25
M
=
36
Step 2 · Find tube length (L)
Use L = fₒ + fₑ
The two focal points meet, so the lenses sit fₒ + fₑ apart.
L
=
900
+
25
L
=
925
mm
Step 3 · Find times more light than the eye (G)
Use G = (D ÷ 7)²
Light gathered goes with the area, so square the ratio of widths.
G
=
(
100
7
)
2
G
=
14.286
2
G
=
204
Check
Put the numbers back in. Both sides should match.
36
=
900
25
✓
925 = 900 + 25 ✓
204
≈
(
100
7
)
2
✓
Topic check
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