Question

2cm high object is placed at distance of 32cm from concave mirror image is real and inverted and 3cm in size find focal length of mirror and position where image is formed

Answer 1

Height of object = h= 2 cm
Height of image= h'= -3cm( as image is real and inverted)
Object distance = -32 cm
Magnification, m = h'/h = -3/2
》-v/u= -3/2
》v/(-32)=3/2
》v= -48 cm
So image is formed at a distance of 48 cm from mirror on same side of object.
Now using mirror formula:
1/v + 1/u = 1/f
》1/(-48) + 1/(-32) = 1/f
》1/f = (-5)/96
》f = (-96)/5 = -19.2 cm

Answer 2

Magnification (n) = h₁/h₂ or - v/u

On substititing values we obtain;

⇒  - 3/2 = - v/(- 32)      [∵3 cm is real image]

⇒ 3/2 × 32 = - v

⇒ - 48 = v

Thus the image is formed on left side where object is placed and is 48 m away from Concave Mirror.

→ 1/f = 1/u + 1/v

→ 1/f = 1/(- 32) + 1/(- 48)

→ 1/f = - 1/32 - 1/48

→ 1/f = (- 3 - 2)/96

→ f = - 96/5 or - 19.2 cm

                  ↓

Focal Length = 19.2 cm

(Negative sign shows that Focus will be on left side)