Question

An object is held at 30cm in front of a convex mirror of focal length 15cm. At what distance from convex mirror should a plane mirror be held so that image in two mirrors coincide with each other?
( ####****** convex mirror has a positive focal length *****###)plz explain the solution as I don't think its correct Answers
We are given

f = -15 cm( ?????? I don't think its correct , convex mirror has a negative focal length)

u = -30 cm

and the image distance will be calculated using

1/f = 1/v + 1/u

or

1/v = 1/f + 1/u

= 1/-15 - 1/30

or

1/v = (-2 - 1)/30 = -3/30

thus, we have

v = -10 cm

now, the image formed would be 30cm behind the convex so the total distance between the object and image will be

= 30cm + 10cm = 40cm.

The plane mirror needs to placed at a distance of 20cm from the object in order for the image to coincide as it will form 20 cm behind it. The total distance would thus have to be 40cm.

Answer 1

length 15cm ...
h=2cm
u=-30cm
f=-15cm
1/v+1/u=1/f
1/v+1/-30=1/-15
1/v=-2+1/30=-1/30
v=-30
the screen must be placed 30cm from the mirror to get the sharp image of it.
m=-v/u=h'/h
-(-30)/30=1
the image formed is real ,inverted and same size as the object

Answer 2

Answer-the plane mirror should be he,d 20 cm to the left of the convex mirror

Explanation-

Given

f=+15cm (covex mirror has positive focus)

u= -30 cm

V=?

1/v = 1/f - 1/u

= 1/15 -(-1/30)

= 1/15 +1/30

= 2+1/30

= 3/30

= 1/10

V is 10 cm and the image will be formed 10cm behind the mirror.

And plane mirror has to be 10 cm in front of the mirror so as to form the image at 10 cm behind the convex mirror

Hope it helped