A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :
- 45 cm
- 15 cm
- 22.5 cm
- 7.5 cm
Answer
(4) 7.5 cm
Solution
Convex mirror: u=-30 cm, f=+30 cm
1v= 1f- 1u= 130+ 130= 115 v=+15 cm
the image is 15 cm behind the convex mirror, i.e. 30+15=45 cm from the object
A plane mirror forms the image as far behind it as the object is in front of it
for the two images to coincide, the plane mirror (facing the object) must be midway between the object and this image:
distance of plane mirror from object = 452=22.5 cm
distance between the mirrors =30-22.5=7.5 cm
Answer: (4)