A candlestick holder has a concave reflector behind the candle.The reflector magnifies a candle -0.75 times and forms an image 4.6 cm away from the...

We know that the real image in a concave reflector is small and inverted  when magnification is -0.75. The position of object for this should be away farther than the centre of curvature and the real invetred image lies between the focus and the centre of cuvature of the reflector. Also the focal length f , object distance u and image distance v from the concave reflector follow the rule:

1/f = 1/u + 1/v......................(1). Since the magnification m =-0.75, the real image is inverted and could be caught on a screen. 

The manification, m = v/u. Or 

v/u = 0.75 Or, u = v/0.75. Substituting this value of u in (1) we get:

1/f = 1/(v/0.75)+1/v = (1/v)(1.75). So ,

the focal length, f =  V/1.75 = 4.6/1.75 = 2.62857 cm.

U = u/0.75 = 4.6/0.75 =  6.13333 cm is the object distance from the concave reflector.