SME
Grade 11 Science · Problem type
A convex mirror
Use this for “A car is 30 cm from a convex mirror with f = −20 cm. Where is its image, and how big?”
Diagram
1/dᵢ
=
1
f
−
1/dₒ
=
1/(−20)
−
1
30
dᵢ = −12 cm
m
=
−dᵢ/dₒ
=
−
−12
30
=
0.4
Virtual, upright and smaller: the rays only seem to come from behind the mirror (dashed).
This is an example. Type your own values to start a new problem.
1
f (cm)
=
1
dₒ (cm)
+
1
dᵢ (cm)
m
Magnification
calculated
hₒ
Object height
example
hᵢ
Image height
calculated
Formulas
1
f
=
1/dₒ
+
1/dᵢ
1/(−20)
=
1
30
+
1/(−12)
m
=
−dᵢ/dₒ
0.4 = −(−12)/30
hᵢ
=
m
×
hₒ
2 = 0.4 × 5
Assumptions
•
A convex mirror spreads light out: f < 0.
•
The image is behind it: virtual, upright and smaller, showing a wide view.
•
dᵢ > 0 is a real image (light really meets there); dᵢ < 0 is a virtual one. m < 0 means upside down.
Step-by-step
WE KNOW
f = −20 cm, dₒ = 30 cm, hₒ = 5 cm
FIND
image distance (dᵢ), magnification (m), image height (hᵢ)
Step 1 · Find image distance (dᵢ)
Use 1/f = 1/dₒ + 1/dᵢ
Take
1/dₒ
from
1
f
,
then
flip.
dᵢ
=
1/(
1
f
−
1/dₒ)
dᵢ
=
1/(1/(−20)
−
1
30
)
dᵢ
=
1/((−0.05)
−
1
30
)
dᵢ
=
1/(−
1
12
)
dᵢ = −12 cm
Step 2 · Find magnification (m)
Use m = −dᵢ/dₒ
The magnification: negative means the image is upside down.
m
=
−(−12)/30
m
=
0.4
Step 3 · Find image height (hᵢ)
Use hᵢ = m × hₒ
The
image
is
m
times
as
tall
as
the
object.
hᵢ = 0.4 × 5
hᵢ = 2 cm
Check
Put the numbers back in. Both sides should match.
1/(−20)
=
1
30
+
1/(−12)
✓
0.4 = −(−12)/30 ✓
2 = 0.4 × 5 ✓
Topic check
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