An object is placed at a large distance in front of a convex mirror of radius of curvature 40 cm.how far is the image behind the mirror?
Answers
R=2f
40=2*f
f=20cm
The image is 20cm behind the convex mirror.
Given: An object is placed at a large distance in front of a convex mirror of radius of curvature 40 cm.
To find: Distance of image behind the mirror
Solution: Let the radius of curvature be r, focal length be f, object distance be u and image distance be v.
r = 40 cm
The relation between radius of curvature and focal length is:
Radius of curvature = 2 × Focal length
=>r = 2 × f
=> 40 = 2f
=> f = 40/2
=> f = 20 cm
A convex mirror has positive focal length. Therefore, f = +20 cm
When an object is placed at a large distance from the mirror, the object distance is said to be at infinite distance.
Therefore, u = -∞(object distance is always negative)
The image distance can be found using mirror formula:
(since 1/∞ = 0)
=> v = 20 cm
Therefore the object is 20 cm behind the mirror.