Science (086) — AI-generated practice question

Given: h = +3 cm, u = –12 cm, f = –8 cm (concave mirror)

(i) Image distance:

Using mirror formula: $\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}$

$$\frac{1}{v} = \frac{1}{f} - \frac{1}{u} = \frac{1}{-8} - \frac{1}{-12} = -\frac{1}{8} + \frac{1}{12} = \frac{-3+2}{24} = \frac{-1}{24}$$

$$v = -24 \text{ cm}$$

The image is formed 24 cm in front of the mirror.

(ii) Height of the image:

$$m = -\frac{v}{u} = -\frac{(-24)}{(-12)} = -2$$

$$h' = m \times h = -2 \times 3 = -6 \text{ cm}$$

Nature of the image: Real, inverted, and enlarged (magnified 2 times).

Source: Chapter 9, Section 9.2.4 – Mirror Formula and Magnification

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• Always assign signs first using New Cartesian Sign Convention: distances in front of mirror are negative, so u = –12, f = –8.
• A negative v confirms the image is real (in front of mirror).
• A negative h′ confirms the image is inverted.
• Examiners award marks for: correct formula application (1 mark), correct v (1 mark), correct h′ and nature (1 mark). Missing the nature statement loses a mark.