Question

the image of an object formed by a mirror is real inverted and it's Magnification-1. if the image is at a distance of 40 cm from the mirror where is the object placed.? where would the image be if the object is moved 20 cm towards the mirror?

Answer 1

Answer:

Since the image formed is real and inverted, the mirror used is concave mirror.

Since the magnification is -1, it tells that the object and image size are the same. This is because 1 represents same size for both and negative sign indicates that the image is real.

We know that, object size is equal to image size only if it is placed at C.

So the object is placed at C in the above case. It is given that it is placed 40 cm from the pole. So C = 40 cm

This implies that Focus is 40/2 = 20 cm.

Now it is said that the object is moved 20 cm further. This means it is present at the focus.

We know that Object placed at focus will give an image at infinity.

Hence the image formed will be located at Infinity distance.

Answer 2

Image formed by the mirror is real and inverted . Also the magnification is given as - 1 . Hence the mirror has to be a concave mirror because no other mirror can show negative magnification.

Also note that the formula for magnification is given as :

Magnification = length of image / length of object ( v/u )

Since magnification is - 1 ,

This means :

- 1 = length of image / length of object

⇒ length of image = - ( length of object )

⇒ I = O

Hence we can identify that the image length is the same as object distance .

Image distance = 40 cm .

u = 40 cm

Given that I = O

I/O = v/u

= I/O = 1

= v/u = 1

= v = u

= v = u = 40 ( since u = 40 given )

Now we apply lens formula here :

1/f = 1/v - 1/u

= 1/f = - 1/40 - 1/40

= 1/f = ( - 1 - 1 )/40

= 1/f = - 2/40

= 1/f = - 1/20

Focal length is 20 cm .

Object is moved 20 cm towards the mirror .

Initially object was at 40 cm .

So now the position will be 40 - 20 = 20 cm .

Hence the object is moved at the focus ( since focal length = 20 cm ) .

Since object is at focus , image should be formed at infinity .

So the image will be  formed at infinity since object is at focus.