Question 29. A convex mirror of radius of curvature 30 cm forms an image that is half the size of the object.
The object distance is :
(1) -15 cm
(2) 45 cm
(3) -45 cm
(4) 15 cm
Answer: (1)
Explanation:
The radius of curvature of the convex mirror is R=30 cm
The focal length is f=\frac{R}{2} f=+15 cm
The image is half the size of the object. So the magnification is m=\frac{1}{2}
For a convex mirror, the image of a real object is virtual and erect.
Hence the magnification is positive.
For a mirror, magnification is given by m=\frac{f}{f-u}
Substitute the values, \frac{1}{2}=\frac{15}{15-u}
Solving, 15-u=30 u=-15 cm
Therefore, the object distance is -15 cm.