Science (086) — AI-generated practice question

Given: f = +10 cm (convex lens), u = −30 cm

Using the lens formula:
$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$$

$$\frac{1}{v} - \frac{1}{-30} = \frac{1}{10}$$

$$\frac{1}{v} = \frac{1}{10} - \frac{1}{30} = \frac{3-1}{30} = \frac{2}{30}$$

$$v = +15 \text{ cm}$$

The image is formed 15 cm on the other side of the lens.

Since v is positive, the image is real and inverted. (The object is placed between F₁ and 2F₁, so the image is beyond 2F₂.)

Source: Light – Reflection and Refraction, Chapter 9, Section 9.3.6

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• Always apply sign convention: u is negative (object on left), f is positive for convex lens.
• The lens formula is $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$; do not mix it up with the mirror formula.
• A positive v means image is on the opposite side of the object → real and inverted for a convex lens.
• Examiners award marks for: correct formula (1), correct substitution with signs (1), correct answer with nature of image (1).