Question

This question deals with spherical mirrors and lenses.

(a) In front of a spherical concave mirror of radius 39 cm, you position an object of height 0.6 cm somewhere along the principal axis. The resulant image has a height of 0.2 cm. How far from the mirror is the object located?

(b) In front of a spherical convex mirror of radius 39 cm, you position an object of height 0.6 cm somewhere along the principal axis. The resultant image has a height of 0.2 cm. How far from the mirror is the object located?

Answer 1

a)

the linear magnification = image height/ object height = - image distance/ object distance

or, -0.2/0.6 = - v/u [image height -ve as it is inverted]

or, 1/3 = v/u

or, v = u/3

and we know the relation for concave mirror:

1/v + 1/u = 1/f

or, 3/u +1/u = - 2/39 [f = -ve ]

or, 4/u = -2/39

or,u = -78 cm

so the object is located 78 cm on the left side of the mirror.

b)

the linear magnification = image height/ object height = - image distance/ object distance

or, 0.2/0.6 = - v/u [image height +ve as upright]

or, 1/3 = -v/u

or, v = -u/3

and we know the relation for concave mirror:

1/v + 1/u = 1/f

or, -3/u +1/u = 2/39 [ focus +ve, image distance +ve as it is right side of mirror and virtual and upright]

or, -2/u = 2/39

or,u = -39 cm

so the object is located 39 cm on the left side of the mirror.