An object of height 6 cm is placed at a distance of 30 cm from the optical centre of a concave lens of focal length 15 cm. Use lens formula to determine:

(a) The distance of image from the optical centre.

(b) The height of the image formed.

Given that, $u = -30 ext{ cm}, f = -15 ext{ cm}, h = 6 ext{ cm}$

(a) Using lens formula, rac{1}{v} - rac{1}{u} = rac{1}{f}

rac{1}{v} = rac{1}{f} + rac{1}{u}

rac{1}{v} = rac{1}{-15} + rac{1}{-30}

rac{1}{v} = rac{-2-1}{30}

rac{1}{v} = rac{-3}{30}

$v = -10 ext{ cm}$

Hence, the distance of image from the optical centre is $10 ext{ cm}$.

(b) Magnification, m = rac{h'}{h} = rac{v}{u}

h' = rac{vh}{u}

h' = rac{(-10)(6)}{-30}

$h' = 2 ext{ cm}$

Hence, the height of the image formed is $2 ext{ cm}$.