Science (086) — AI-generated practice question

Given: R = 40 cm, so f = R/2 = −20 cm (concave mirror); object height h = 5 cm; u = −20 cm

Mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$

$$\frac{1}{v} + \frac{1}{-20} = \frac{1}{-20}$$

$$\frac{1}{v} = -\frac{1}{20} + \frac{1}{20} = 0 \implies v = \infty$$

Since the object is placed exactly at the focus (u = f = −20 cm), the reflected rays are parallel and no image is formed at a finite distance (image at infinity).

Magnification: $m = -\frac{v}{u}$ → undefined (image at infinity).

Nature: Real and inverted (for any finite screen, image cannot be obtained).

Source: Light – Reflection and Refraction, Table 9.1; Mirror Formula section

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• For a concave mirror, both f and u are negative by sign convention (distances measured opposite to incident light).
• R = 40 cm → f = −20 cm. Since u = −20 cm = f, the object is at the focus, so the image forms at infinity — this is a standard result from Table 9.1.
• Examiners award marks for: correct f, correct substitution, correct conclusion (image at infinity), and nature statement. Don't leave out the sign convention step.