Answer:
The object should be placed 180/3 cm in front of the mirror in order to form a real image having half its linear dimension.
Step-by-step explanation:
To find the position of an object that will form a real image having half its linear dimension when reflected in a spherical mirror, we can use the mirror equation. The mirror equation relates the distance of the object from the mirror (d_o), the distance of the image from the mirror (d_i), and the radius of curvature of the mirror (R):
1/d_o + 1/d_i = 2/R
In this case, we are given that the radius of curvature of the mirror is 180 cm, and we want to find the distance of the object from the mirror (d_o). We are also given that the image will have half the linear dimension of the object, which means that the image is twice as far away as the object. Therefore, the distance of the image from the mirror (d_i) is 2*d_o.
Substituting these values into the mirror equation gives:
1/d_o + 1/(2*d_o) = 2/180
Solving this equation for d_o gives:
d_o = 180/3 cm