An object is placed a certain distance from convex mirror of focal length 20cm. Find distance of the object if the image obtained is magnified four times.
Given that the focal length of the mirror is 20cm and the image obtained is magnified four times, we can use the mirror formula to find the distance of the object.
The mirror formula is given by:
1/f = 1/v + 1/u
Where:
f = focal length of the mirror = 20cm
v = image distance
u = object distance
Since the image obtained is magnified four times, the magnification is given by:
Magnification = -v/u = 4
Therefore, v = -4u
Substitute this value of v in the mirror formula:
1/20 = 1/(-4u) + 1/u
Multiplying throughout by 20u to clear the fractions:
u = -80 + 20
u = -60 cm
Therefore, the object is placed at a distance of 60 cm from the convex mirror.