Question

Size of image of an object by a mirror having a focal length of 20 cm is observed to be reduced to1/3 of its size. At what distance from the mirror the object has been placed? What is the nature of image and the mirror​

Answer 1

Answer:

Hi there! Hope this answer helps!!!

So, the focal length = 20 cm

The mirror can be either convex or concave. Hence we shall take help from the magnification

-v/u = 1/3

Hence u = -3v

Let us find the image distance first,

1/f = 1/v + 1/u

Hence,

1/20 = 1/v + 1/-3v

= 3- 1 / 3v = 1/20

Hence,

20 = 3v/2

v = 40/3

Object distance = - 3v

= - 3 x 40/3

Hence object distance is -40 cm.

Since we don't know much about the type of mirror, since it can be both concave and convex, the nature of the image is : real/virtual, diminished and erect/inverted.

Hope this helps!!

Side note : Please specify the type of mirror since it is quite hard to solve without finding the type. It can be Concave - since it produces a diminished real image and it can also be Convex - since it produces a diminished virtual image.

Answer 2

Answer:

-40cm,diminished,convex mirror

Explanation:

given-magnification=1/3

f=20cm

using mirror formula= 1/f=1/v +1/u

1/20=1/v +1/u

equating the eqaution we get v=20u/u-20............<1>

using magnification formula=m=-v/u

1/3= -20u/u-20*u.................(from eq 1)

by solving the above u= -40cm