find the position of an object for which a convex mirror of radius of curvature 30 cm from a virtual image at 6 cm behind the mirror
Answers
Answer:
An object is placed at a distance of 36 cm from a convex mirror. A plane mirror is placed in between so that the two virtual images so formed coincide. If the plane mirror is at a distance of 24 cm from the object,
To find the radius of curvature of the convex mirror.
Solution:
As per the given criteria,
object distance from the convex mirror, u=36cm
distance of plane mirror from the object, d=24cm
So,
The distance of plane mirror from the convex mirror will be
34−12=12cm
The image formed by the plane mirror will be at a distance of 24cm from the plane mirror and 12 cm from the convex mirror.
Since both the images should coincide therefore the convex mirror will form image at a distance of 12cm from itself.
Therefore, u=−36cm
v=12cm
Applying the lens formula, we get
f
1
=
v
1
+
u
1
⟹
f
1
=
12
1
+
(−36)
1
⟹
f
1
=
36
3−1
⟹f=18cm
And we know the radius of curvature, R=2f=2×18=36cm
Answer:
- 10cm
Explanation:
Since the object is within the focal length of the concave mirror, the image is virtual, erect and magnified.