An object is placed in front of a concave and convex mirror as shown below. Determine the value of ‘x’ if the virtual images are formed on the same plane. The focal length of the concave and convex mirrors are 40 cm and 6.5 cm, respectively.
(a) 15cm
(b) 20cm
(c) 10cm
(d) 25cm
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Answer:
Correct option is
C
6cm behind convex mirror, virtual
According to given problem, for concave mirror,
u=−15 cm and f=−10 cm
v
1
+
−15
1
=
−10
1
, i.e., v=−30 cm
i.e., concave mirror will form real, inverted, and enlarged image I
1
of object O at a distance of 30 cm from it, i.e., at a distance 40−30=10 cm from the convex mirror.
For convex mirror, the image I
1
will act as an object and so for it u=−10 cm and f=+15 cm.
v
1
+
−10
1
=
15
1
, i.e., v=+6 cm
So, final image I
2
is formed at a distance of 6 cm behind the convex mirror and is virtual as shown in figure.
Explanation:
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