Optics and resulting image

Question

If a decorative mirror has a .2m focal length and is concave and a candlestick that is 0.03m tall is placed .3m in front of the mirror... What is the position and magnification of the image for the mirror? Is the image magnified/diminished, real or virtual and is it upright or diminished?

Answer 1

1/F = 1/d + 1/f (mirror formula). We have F = 0.2 m; d = 0.3 m, f is distance from image to mirror.

1/f = 1/0.2 - 1/0.3 = 0.1/0.06 = 5/3. So f = 0.6 m. Magnification is f/d = 0.6/0.3 = 2. So image is 0.03 ·2 =

0.06 m tall and real and diminished