Question

The radius of a convex spherical mirror is 33.0 cm. A toy 1.6 cm high is located 10.0 cm in front of the mirror.

a) What is in centimeters the focal length of the mirror?

b) What is in centimeters the distance separating the position of the formed image from the mirror?

c) What is in centimeters the height of the image? (express an upright image as positive and a flipped image as negative)

Answer 1

As f = r/2

f = -33.0/2 cm = -16.5 cm, negative because it is a convex mirror [PART A]

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    -16.5   cm
do = object distance =    10   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -6.23    cm [ANSWER, PART B, 6.23 cm to the back of the mirror]
      
Thus, the magnification, m = -di/do,      
      
m =    0.622641509  
      
Thus, as      
hi =    1.6   cm
      
And hf = m * hi, then      
      
hf =    0.996   cm [PART C ANSWER]