Science (086) — AI-generated practice question

Given: Object height (h) = 3 cm, u = −12 cm, f = +8 cm (convex lens)

Using Lens Formula:
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$
$$\frac{1}{v} - \frac{1}{-12} = \frac{1}{8}$$
$$\frac{1}{v} = \frac{1}{8} - \frac{1}{12} = \frac{3-2}{24} = \frac{1}{24}$$
$$v = +24 \text{ cm}$$

Magnification:
$$m = \frac{v}{u} = \frac{24}{-12} = -2$$

Height of image:
$$h' = m \times h = -2 \times 3 = -6 \text{ cm}$$

The image is 6 cm tall and inverted (negative sign indicates inversion). The image is real and magnified, formed beyond 2F₂.

Source: Chapter 9, Section 9.3.5 & 9.3.6

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• Always apply sign convention: u is negative (object on left), f is positive for convex lens.
• A negative image height (h′) means the image is inverted; negative magnification confirms this.
• The object is between F and 2F (12 cm is between 8 cm and 16 cm), so from Table 9.4, the image must be real, inverted, and enlarged — consistent with our result.
• Examiners award marks for: correct formula use (1), correct v (1), correct h′ with erect/inverted conclusion (1).