Question

2. A 10-cm high object is placed in front of a convex mirror with focal length 20 cm. Determine the image height if the object distance is (a) 10 cm (b) 30 cm (c) 40 cm (d) 50 cm ​

Answer 1

Given : A 10 cm high object is placed in front of a convex mirror with focal length 20cm.

To find : the image height if the object distance is (a) 10cm (b) 30cm (c) 40cm (d) 50 cm

solution : let's create general formula to find the height of image.

object distance = - u

height of object = +O

and focal length of mirror = +f

now using formula, 1/v + 1/u = 1/f

⇒1/v + 1/-u = 1/+f

⇒1/v = 1/f + 1/u = (f + u)/fu

⇒v = fu/(f + u)

now magnification, m = -v/u

⇒height of image/height of object = -[+fu/(f + u)]/-u

⇒height of image = f/(f + u) × O

now find height of image using above formula.

(a) u = 10cm, f = 20cm, O = 10cm

so, Height of image = 20/(20 + 10) × 10 = 20/3 cm

(b) u = 30cm , f = 20cn and O = 10cm

so, Height of image = 20/(20 + 30) × 10 = 4 cm

(c) u = 40cm , f = 20cm and O = 10cm

so, Height of image = 20/(20 + 40) × 10 = 10/3 cm

(d) u = 50cm, f = 20cm and O = 10 cm

so, Height of image = 20/(20 + 50) × 10 = 20/7 cm