Answer:
The image is formed 40/3 cm behind the mirror, and its height is 3.33 cm.
Step-by-step explanation:
To find the image distance and height, we can use the mirror formula and magnification formula:
Mirror formula:
1/f = 1/d_o + 1/d_i
Magnification formula:
m = -d_i/d_o
Where f is the focal length, d_o is the object distance, d_i is the image distance, and m is the magnification.
Since the mirror is concave, the focal length is negative and given by:
f = -R/2
where R is the radius of curvature.
Substituting the values, we get:
f = -16/2 = -8 cm
d_o = -40 cm (since the object is in front of the mirror, the distance is negative)
Substituting these values into the mirror formula:
1/-8 = 1/-40 + 1/d_i
Simplifying:
-1/8 = -5/200 + 1/d_i
-1/8 = -1/40 + 1/d_i
-3/40 = 1/d_i
d_i = -40/3 cm
Since the image distance is negative, the image is formed behind the mirror.
Using the magnification formula:
m = -d_i/d_o
m = (-40/3)/(-40) = 1/3
Therefore, the image height is one-third the object height:
h_i = m * h_o
h_i = (1/3) * 10 cm = 3.33 cm
So, the image is formed 40/3 cm behind the mirror, and its height is 3.33 cm.