An object is placed at (i) 10cm (ii) 5 cm in front of a concave mirror of radius of curvature 15cm. Find the position, nature and magnification of the image in each case.

Explanation

f = `(-15)/(2) = - 7.5` cm
i. u = -10 cm
` because (1)/(v) + (1)/(u) = (1)/(f) " " (1)/(v) + (1)/(-10) = (1)/(-7.5) " " therefore v = (-10xx - 7.5)/(-2.5) = - 30 ` cm
image is formed at 30 cm from the object on the same side of the object.
m = `(-v)/(u) = (-(30))/((-10)) = -3`
Image is magnified, real and inverted.
(ii). u ` = - 5 cm , (1)/(v) + (1)/((-5)) = (1)/((-7.5)) " " therefore v = (- 5 xx - 7.5)/(2.5) = 15` cm
Image is formed at 15 cm behind the mirror, `m = (-v)/(u) = (-15)/(-5) = 3 `
Image is magnified , erect and virtual.