Question

An object is placed in front of a concave mirror at a distance of distance of 24 cm.The focal length of the mirror is 10 cm from the vertex. The object is 2.52 cm in height. Discuss the image characteristics? What is the size of the image? What is the distance of the image from the vertex?

Answer 1

u= 24

f=10

h = 2.52

applying mirror formula

1/v + 1/u = 1/f

v= f*u/(u-f)

=17.142 cm ( distance of image from the vertex)

m=- v/u = h'/h ( magnification)

so h' = -v*h/u= 17.142*2.52/24 = 1.8 cm

image will be inverted and diminished

Answer 2

object distance u = 24 cm

f = 10 cm

object height y= 2.52 cm

from the relation

1/u + 1/v = 1/f

1/24 + 1/v = 1/10

v = 17.142 cm

as image distance is +ve it is real image

and magnification m=-v/u = y'/y

size of the image y' = -17.142*2.52/24 = -1.8 cm

as image height is -ve it is a inverted and enlarged image

distance from vertex v = 17.142 cm