An object is placed at a distance of 15 cm in front of concave mirror of focal length 5 cm. At what distance in front of mirror is the image formed -
a) 5 cm
b) 7.5 cm
c) 10 cm
d) 12.5 cm
Correct answer please...
Answers
ANSWER
It can seen from the figure that, if the object is placed at a distance x from the concave mirror, its distance from the plane mirror will be (22.5−x). So plane mirror equal and erect image of object at a distance (22.5−x) behind the mirror. Now according to the given problem, the image coincided with the image formed by the plane mirror, therefore for concave mirror.
v=−[22.5+22.5−x]=−(45−x)
and object distance
u=−x
given focal length is
f=−10
So using mirror formula,
v
1
+
u
1
=
f
1
−(45−x)
1
+
−x
1
=
−10
1
⟹
45x−x
2
45
=
10
1
x
2
−45x+450=0
(x−30)(x−15)=0
Hence x=30cm or x=15cm
.
But as the distance between the two mirror is 22.5, x=30 is not admissible . So the object must be at a distance of 15 cm from the concave mirror
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