Answer: approximately 8.13 cm from the concave mirror and the magnification of the mirror is approximately 1.85.
Step-by-step explanation:
To solve this problem, we can use the mirror equation and the magnification formula for concave mirrors.
(a) The mirror equation is given by:
1/f = 1/do + 1/di
where f is the focal length of the mirror, do is the object distance, and di is the image distance.
Given:
f = radius of curvature/2 = 35.5 cm / 2 = 17.75 cm
di = -15.0 cm (negative sign indicates a virtual image)
Substituting these values into the mirror equation, we can solve for do:
1/17.75 = 1/do - 1/15.0
Simplifying the equation:
1/do = 1/17.75 + 1/15.0
1/do = (15.0 + 17.75)/(17.75 * 15.0)
1/do = 32.75/(266.25)
1/do ≈ 0.123
Taking the reciprocal of both sides:
do ≈ 1/0.123
do ≈ 8.13 cm
Therefore, the position of the object is approximately 8.13 cm from the concave mirror.
(b) The magnification (m) of the mirror can be determined using the formula:
m = -di/do
Substituting the given values:
m = -(-15.0 cm) / 8.13 cm
m ≈ 1.85
Therefore, the magnification of the mirror is approximately 1.85.