SME
Grade 5 Science · Problem type
Two flashlights at different distances
Use this for “Why does a flashlight look dimmer farther away?” and why the sun looks brightest.
Diagram
Nearer distance: 50 cm
Times as far: 4
Farther distance: 200 cm
The lit circle is 4 times as wide.
It covers 4 × 4 = 16 squares, so each square gets 1/16 of the light.
Times as much wall lit: 16
This is an example. Type your own values to start a new problem.
Nearer distance (cm)
×
Times as far
=
Farther distance (cm)
Times as much wall lit
worked out (not typed)
Formulas
50 × 4 = 200
Nearer distance × times as far = farther distance
4 × 4 = 16
Times as far × times as far = times as much wall lit
Assumptions
•
Two of the same flashlight give the same light.
•
Twice as far, the lit circle is twice as wide and twice as tall: 4 times the wall.
•
The same light spread over more wall looks dimmer.
•
Stars work the same way: the sun is a star that is very close to us.
Step-by-step
WE KNOW
Nearer distance: 50 cm
Times as far: 4
FIND
farther distance, times as much wall lit
Step 1 · Find farther distance
50 × 4 = ?
Nearer distance × times as far = farther distance
That many times the nearer distance.
Farther distance = 200 cm
Step 2 · Find times as much wall lit
4 × 4 = ?
Times as far × times as far = times as much wall lit
The lit circle is that many times as wide and as tall.
Times
as
much
wall
lit
=
16
(each
part
of
the
wall
gets
1
16
as
much
light:
dimmer)
Check
Put the numbers back in. Both sides should match.
50 × 4 = 200 ✓
4 × 4 = 16 ✓
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The sun as a star; brightness and distance
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Patterns of Earth and sky: shadows, day and night, stars
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