JAMB - Physics (2025 - No. 62)

A concave mirror of focal length 20cm produces an erect image that is four times the object, the object distance from the mirror is
less than 20cm
Between 20cm and30cm
Between 30cm and 40cm
Greater than 40cm

Explanation

A. Less than 20 cm

For a concave mirror, an erect image is virtual (behind the mirror) and forms when the object is placed between the pole and focus (\( u < f \)).

Magnification:
\(m = +4 \quad (\text{erect, so positive})\)

Using the mirror formula:
\(\frac{1}{v} + \frac{1}{u} = \frac{1}{f}\)

Given \( f = -20 \, \text{cm} \) (concave), \( u \) is negative.

Since \( m = -\frac{v}{u} \):
\(v = -m u = -(+4)u = -4u\)

Substituting into the mirror formula:
\(\frac{1}{-4u} + \frac{1}{u} = \frac{1}{-20}\)

Combining the fractions:
\(\frac{3}{4u} = \frac{1}{-20}\)

Thus, solving for \( u \):
\(3 \cdot -20 = 4u \quad \Rightarrow \quad u = -15 \, \text{cm}\)

Object distance \( |u| = 15 \, \text{cm} < 20 \, \text{cm} \).

Thus, it is less than 20 cm.

OR

A concave mirror only gives an erect, magnified image when the object is placed between the mirror and its focal point. Since the focal length is 20 cm, the object must be closer than 20 cm to the mirror.

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