Reflection of Light in Curved Mirrors
Senior 2 · Physics
Reflection of Light in Curved Mirrors
Lesson 3 of 4
25 min
A ray diagram is quick, but its accuracy is limited by your ruler and your drawing. Optical engineers who design headlamps, projectors and telescopes need exact positions. The mirror equation gives the image position and size by calculation, and it is a favourite in national examinations because it tests both algebra and understanding.
Let u be the distance of the object from the pole, v the distance of the image from the pole, and f the focal length. Then
1/f = 1/u + 1/v
If your answer for v is negative, the image is virtual, upright and behind the mirror. If v is positive, the image is real, inverted and in front of the mirror.
The magnification m tells you how much bigger or smaller the image is:
m = image height ÷ object height = v ÷ u
Use the sizes (ignore the minus sign) when you calculate m. If m > 1 the image is magnified; if m < 1 it is diminished; if m = 1 it is the same size.
An object is 30 cm in front of a concave mirror of focal length 10 cm. Find the image.
1/v = 1/f − 1/u = 110 − 130 = 330 − 130 = 230, so v = +15 cm.
m = v/u = 1530 = 0.5.
v is positive, so the image is real and inverted, 15 cm in front of the mirror, and half the size of the object. (Check with the table: object beyond C at 20 cm gives an image between F and C. ✓)
An object 4.0 cm tall is 5.0 cm in front of the same concave mirror (f = 10 cm).
1/v = 110 − 15 = 110 − 210 = −110, so v = −10 cm.
m = 105 = 2, so the image is 2 × 4.0 = 8.0 cm tall.
v is negative, so the image is virtual and upright, 10 cm behind the mirror, and twice the size of the object: the shaving-mirror case.
An object is 30 cm in front of a convex mirror of focal length 15 cm. Because the mirror is convex, f = −15 cm.
1/v = 1/f − 1/u = −115 − 130 = −230 − 130 = −330, so v = −10 cm.
m = 1030 = 13. The image is virtual, upright, one third the size of the object, and 10 cm behind the mirror.
A concave mirror forms a real image on a screen 36 cm from the mirror when a lamp is 12 cm from it.
1/f = 112 + 136 = 336 + 136 = 436, so f = 9.0 cm, and R = 2f = 18 cm.
Tip
A four-line routine that earns full marks
The classic error is to forget to take the reciprocal at the end: 1/v = 230 means v = 15 cm, not 230 cm.
An object is 40 cm from a concave mirror of focal length 10 cm. Find the image position and the magnification.
Solution: 1/v = 110 − 140 = 340, so v ≈ 13.3 cm (real). m = 13.3/40 ≈ 0.33: real, inverted, diminished.
An object is 15 cm from a concave mirror of focal length 10 cm. Find the image.
Solution: 1/v = 110 − 115 = 130, so v = 30 cm. m = 3015 = 2: real, inverted and magnified, beyond C. (This matches the scale drawing in the last lesson.)
An object is 20 cm in front of a convex mirror of focal length 20 cm. Find the image.
Solution: f = −20 cm. 1/v = −120 − 120 = −220, so v = −10 cm. m = 1020 = 0.5: virtual, upright, half-size, 10 cm behind the mirror.
Umutoni's make-up mirror is concave with f = 25 cm. Her face is 15 cm from it. Where is the image, and how much is it magnified?
Solution: 1/v = 125 − 115 = 375 − 575 = −275, so v = −37.5 cm (virtual, behind the mirror). m = 37.5/15 = 2.5: upright and 2.5 times larger.
Remember
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