A square of side is located at a distance of from a concave mirror of the focal length of . The center of the square is at the axis of the mirror and the plane is normal to the axis of the mirror. The area enclosed by the image of the square is
Step 1: Given data
Height of the object:
Width of the object:
Distance of object from mirror:
Focal length:
Let distance of image from mirror be
It is given that the rods of the mirror is normal to the square and thus the mirror is parallel to the square.
Step 2: Formula used
Mirror formula is given as,
The magnification produced by a mirror,
where is the height of the image and is the height of the object
Step 3: Solution
Substituting the values in the mirror formula,
Therefore magnification is,
The negative sign of the height indicates that the image is inverted
Similarly,
Therefore, the area of the image formed
Hence, the area enclosed by the image of the square is .