An object of 1cm^2 face area is placed at a distance of 1.5m from a screen. How far from the object should a concave mirror be placed so that it forms 4cm^2 image of object on the screen? Also, calculate the focal length of the mirror.
Please give the explanation as soon as possible it's urgent
Answers
Answer:
In the magnification equation, the variables are the image height and object height and not the area. In the given values in the problem, both the areas are perfect square so we can assume that the object is a square. The object height and image height are therefore equal to
h
o
=
√
1
c
m
2
=
1
c
m
h
i
=
√
4
c
m
2
=
2
c
m
Using these values, we can get the magnification of the mirror.
M
=
h
i
h
o
M
=
2
c
m
1
c
m
M
=
2
The distance between the object and the screen is the sum of the object distance and image distance.
d
o
+
d
i
=
1.5
m
d
o
+
d
i
=
1.5
m
⋅
100
c
m
1
m
d
o
+
d
i
=
150
c
m
d
i
=
150
c
m
−
d
o
d
i
=
−
(
150
c
m
−
d
o
)
Since the screen is located behind the mirror, the image distance is negative so the magnification is positive.
M
=
−
d
i
d
o
2
=
−
d
i
d
o
Substitute the expression for image distance that we got.
2
=
−
[
−
(
150
c
m
−
d
o
)
]
d
o
2
=
(
150
c
m
−
d
o
)
d
o
2
=
150
c
m
d
o
−
1
2
+
1
=
150
c
m
d
o
3
=
150
c
m
d
o
3
(
d
o
)
=
150
c
m
d
o
=
150
c
m
3
d
o
=
50
c
m