The origin of x and y coordinates is the pole of a concave mirror of focal length 20 cm. The x- axis is
the optical aixs with x > 0 being the real side of mirror. A point object at the point (25 cm, 1 cm) is
moving with a velocity 10 cm/s in positive x – direction. The velocity of the image in cm/s is
approximately
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Answered by
0
Answer:
Explanation:
The correct option is C
−
40
^
i
+
2
^
j
Given,
Focal length,
f
=
−
20
cm
Object distance,
u
=
30
cm
Initial height,
h
0
=
1
cm
Velocity of image along positive
x-axis
,
d
u
d
t
=
10
cm/sec
If
v
is the image distance, then
1
v
+
1
u
=
1
f
Substituting the values, we get
1
v
−
1
30
=
−
1
20
⇒
v
=
−
60
cm
For the velocity of image along the
x-axis
we can use,
d
v
d
t
=
−
v
2
u
2
(
d
u
d
t
)
Substituting the values,
v
x
=
−
(
60
30
)
2
×
10
⇒
v
x
=
−
40
cm/sec
Linear magnification
m
=
f
f
−
u
⇒
d
m
d
t
=
−
[
f
(
f
−
u
)
2
]
(
d
u
d
t
)
Substituting the values,
⇒
d
m
d
t
=
−
(
20
)
(
−
20
+
30
)
2
×
10
⇒
d
m
d
t
=
−
2
Velocity of image along
y-axis
v
y
=
d
h
i
d
t
=
−
(
d
m
d
t
)
h
0
⇒
v
y
=
(
−
1
)
×
(
−
2
)
×
1
=
2
cm/s
Negative sign indicates that
h
i
decreases with time.
Velocity of the image
v
I
=
v
x
^
i
+
v
y
^
j
∴
v
I
=
−
40
^
i
+
2
^
j
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