u = 30 cm (negative)
f = 15 cm (negative)
Mirror formula:
1\over u + 1\over v = 1\over f⇒ – 1\over 30 + 1\over v = – 1\over 15
⇒ 1\over v = – 1\over 15 + 1\over 30
⇒ 1\over v = -2 + 1\over 30
⇒ 1\over v = -1\over 30
⇒ v = 30 cm
Hence, the image is formed at 30 cm in front of the mirror
(b) Magnification
Image\ size \over Object\ size = Image\ distance \over Object\ distance⇒ I \over 4 =- 30 \over 30
⇒ I = – 30 \over 30 × 4 = – 4 cm
Hence, length of image = 4 cm
Negative sign represents that the image is inverted.