an object one centimetre high produces a real image -1.5 cm high when placed at a distance of 15 cm from a concave mirror calculate the position of the image and magnification
Answers
Image height H2 = 1.5cm
Object distance u = -15cm (object is taken behind the mirror)
Since, magnification = image height/object height,
M = H2/H1 = 1.5/1 = 1.5
Since, also, magnification = image distance/ object distance
=> 1.5 = image distance/-15
=> image distance = -22.5cm
=>22.5 cm behind the mirror
an object one centimetre high produces a real image -1.5 cm high when placed at a distance of 15 cm from a concave mirror calculate the position of the image and magnification
answer
See below.
Position:
−
0.05714
m
Magnification:
0.28571
Explanation:
Since we are given that the height of the object is
0.03
meters high and is placed
0.2
meters away from a convex mirror with focal length
−
0.08
meters, we can write out are givens in SI units as:
d
o
b
j
=
.2
h
o
b
j
=
.03
since the image created by convex mirrors are always upright and thus have a positive height value
f
=
−
0.08
since the focal length of convex mirrors are negative
Consider the following two formulas:
Lensmaker's Formula:
1
f
=
1
d
o
b
j
+
1
d
i
m
g
Magnification Equation:
M
=
h
i
m
g
h
o
b
j
=
−
d
i
m
g
d
o
b
j
To determine the image's position, we can solve for
d
i
m
g
in the Lensmaker's Formula with variables only, then plug in the given values to solve:
1
d
i
m
g
=
1
f
−
1
d
o
b
j
Taking the reciprocal of both sides, we get:
d
i
m
g
=
1
1
f
−
1
d
o
b
j
Now, we can substitute the given values of
d
o
b
j
and
f
to solve:
d
i
m
g
=
1
1
−
0.08
−
1
0.2
=
−
0.05714
m
Using this value, we can find the magnification of the convex mirror:
M
=
−
d
i
m
g
d
o
b
j
=
−
−
0.05714
0.2
=
0.28571
which has no units
I hope it will help you
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