Science (086) — AI-generated practice question

When the object is placed at the focus F₁ of a convex lens (u = –f), substituting in the lens formula:

$$\frac{1}{v} - \frac{1}{u} = \frac{1}{f} \implies \frac{1}{v} = \frac{1}{f} + \frac{1}{u} = \frac{1}{f} - \frac{1}{f} = 0$$

So v = ∞. The image is formed at infinity.

Physical reason: A ray passing through the focus refracts and emerges parallel to the principal axis (as stated in ray diagram rules). All such refracted rays are parallel and never converge, so the image forms at infinity.

Practical application: This principle is used in torches/searchlights/vehicle headlights — a bulb placed at the focus of a concave reflector (or lens) produces a powerful parallel beam of light.

Source: Chapter 9, Section 9.3.4 (Table 9.4) and Section 9.3.5

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• The lens formula substitution showing v = ∞ earns the formula/calculation mark.
• The physical reason (parallel refracted rays never meet) links to the ray diagram rule from Section 9.3.5(ii) — examiners expect this connection.
• For the application, the textbook explicitly mentions torches/searchlights/headlights in the concave mirror section; the same optical principle applies. Write one specific application — do not list many.
• Keep the formula step brief but shown; board examiners award a mark for it.