An object is placed in front of a concave mirror whose radius of curvature is 12cm. If the magnification of…

Analyze the question: A concave mirror has R = 12 cm, so f = R/2 = 6 cm. The magnification is 1.5, and we need the object distance u.

Concept:

• Mirror formula: 1/f = 1/u + 1/v
• Magnification: m = v/u (using magnitudes)

A concave mirror gives a magnified image in two cases, and the question doesn't say which one applies.

Case 1: Real, inverted image (object between f and 2f) Here v = 1.5u, so 1/6 = 1/u + 1/(1.5u) = (1 + 0.6667)/u = 1.6667/u u = 6 × 1.6667 = 10 cm

Case 2: Virtual, upright image (object inside f) Here v = −1.5u, so 1/6 = 1/u − 1/(1.5u) = 0.3333/u u = 2 cm

The 2 cm answer is not among the options. The only option that fits is 10 cm.

Check for u = 10 cm: 1/v = 1/6 − 1/10 = (5 − 3)/30 = 1/15, so v = 15 cm. m = v/u = 15/10 = 1.5 ✓

Tip: For a concave mirror, the general shortcut is u = f(m + 1)/m when the image is real. Here u = 6 × 2.5/1.5 = 10 cm. Always compute f = R/2 first, and remember that a magnification greater than 1 can come from a real or a virtual image, so check which result appears among the options.