An object is placed in front of convex mirror of radius of curvature of 20cm.its image is formed 8cm behind the mirror.find the distance of the object from the mirror answer with diagram
Answers
Answer:
mirror or radius of curvature 40 cm.
To find the distance at which the plane mirror should be placed such that the images due to the mirror and the plane mirror are in the same plane
Solution:
According to the given criteria,
Object distance from convex mirror, u=−20cm
Radius of curvature of convex mirror, R=40cm
Focal length of the convex mirror, f=
2
R
=
2
40
=20cm
Now applying the mirror formula we get,
f
1
=
v
1
+
u
1
⟹
20
1
=
v
1
+
−20
1
⟹
v
1
=
20
1
+
20
1
⟹v=10cm
So the distance is formed on the opposite side of the object at a distance of 10 cm from the mirror as shown in above fig.
The distance between object and image is u+v=20+10=30cm
When plane mirror is placed in front of object and in order to get image at same position as convex mirror, the mirror should be place at
2
30
=15cm, as in plane mirror the object distance from mirror is equal to image distance from the plane mirror (refer above fig).
Hence the distance at which the plane mirror should be placed such that the images due to the mirror and the plane mirror are in the same plane = 15cm
