in the formula 1 / f =1 /2 + 1 /v find u when v = 15 cm and F = 5 cm
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Given object is at a distance (u=−20cm) from a concave mirror of focal length f=−15cm.
We shall find image (v) distance using mirror formula:
v
1
+
u
1
=
f
1
⇒
v
1
=
f
1
−
u
1
=(
−15
1
)−(
−20
1
)
=
60
−4+3
=−
60
1
⇒v=−60cm
now consider object and image velocities be v
o
kvi respectively, where
v
o
=
dt
du
×vi=
dt
dv
where v
o
=5m/s (given)
From mirror formula,
v
1
+
u
1
=
f
1
different wrt time
−
v
2
1
dt
dv
−
u
2
1
dt
du
=0 (as f is constant)
⇒−
v
2
1
v
1
n
=
u
2
1
v
o
=0
⇒v
1
=−(
u
2
v
2
)v
o
Putting values of v, u and v_o from above:
⇒VI=−(
20
2
60
2
)×5=−45 m/s
∴ Speed of image =45 m/s ans.
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