Question

A concave mirror produces a real image 1 cm tall of an object 2.5 cm tall placed 5 cm from the mirror. Find the position of image and the focal length of the mirror

Answer 1

Answer:

The image is formed 20 cm in front of the mirror.   Focal Length = - 4 cm

Explanation:

h2 = 1cm = 10mm (real image), h1 = 2.5mm, u = -5cm = -50mm

m = - h2/h1

m = - (10/2.5)

m = -4

and we know that

m = - (v/u)

-4 = - (v/(-50)

v = - 200 mm

v = - 20 cm

The image is formed 20 cm in front of the mirror.

And,

1/v + 1/u = 1/f

1/-20 + 1/-5 = 1/f

1/f = -25/100

f = - 4 cm

Answer 2

Answer:-20 cm,-4 cm

h2 = 2.5mm = 0.25cm

u = -5 cm

m = h1/h2 = -v/u

-1/0.25 = -v/ -5

-4 = v/5

v =-20

So, position of image = 20cm in front of mirror

now, using mirror formula , we get

1/f = 1/v + 1/u

1/f = 1/-20 + ( 1/ -5)

1/f = -1/20 + (-1/5)

1/f = -1 + (-4) / 20

1/f = -5/20 = -1/4

f = -4