Question

A concave mirror (f₁ = 14.6 cm) and a convex mirror (f₂ = ?6.70 cm) are facing each other and are separated by a distance of 34.0 cm. An object is placed between the mirrors and is 17 cm from each mirror. Consider the light from the object that reflects first from the concave mirror and then from the convex mirror. What is the distance of the image (d_i2) produced by the convex mirror

Answer 1

Note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    14   cm
do = object distance =    17.6   cm
di = image distance      
      
Thus, solving for di,      
      
di =    68.44444444   cm

which is actually projected at the back of the convex mirror, 35.2 - 68.44 = -33.344 cm = do.

Thus, note that      
      
1/f = 1/do + 1/di      
      
where      
      
f = focal length =    -5.6   cm
do = object distance =    -33.244444   cm
di = image distance      
      
Thus, solving for di,      
      
di =    -6.73   cm