Question

an object 3cm is placed at a distance of 8 cm from a concave mirror which produces a virtual image 4.5 centimetre high what is the focal length of the mirror​

Answer 1

Answer:

focal length of the mirror (f) = -24 cm

Explanation:

distance of object from the mirror (u) = - 8 cm

height of object(h) = 3 cm

As the nature of image is virtual so that's why height of image will be positive.

So, height of image(h') = 4.5 cm

Let distance of image from denoted by = v

As we know,

Magnification of the mirror is ratio of height of image to the height of object. that is given by

m = (height of image)/(height of object)         -------------------(equation 1)

Also we know

m = -v/u                    -------------------------------------(equation 2)

From equation (1)  and  equation (2) we get,

h'/h = (-v/u)

4.5/3 = (-v/(-8)

v  = 12 cm

So, distance of image from mirror(v) = 12 cm,

Positive sign of distance image denotes that nature of image will virtual and image will form on the right side of the mirror.

Now using mirror formula

1/f = 1/v +1/u

1/f = (u+v)/uv

f = uv/(u+v)

f = (-8*12)/(-8+12)

f = (-96/4)

f = -24 cm

So focal length of the given concave mirror will be -24 cm.