Physics questions on concave mirrors?

Question

1. A convace shaving mirror has a focal lenght of 33cm. Calculate the image position of a cologne bottle placed in front of the mirror at a distance of 93 cm. Calculate the magnification of the image. Is the image real or virtual. Is the image inverted or upright. How large is the image formed in respect to the object?

2. A pen places 11 cm from a concave spherical mirror produces a real image 13.2 from the mirror. WHat is the focal length of the mirror. WHat is the magnification of the image. If the pen is placed 27.0 cm from the mirror, what is the new position of the image? What is the magnification of the new image? Is the new image real or virtual?

Answer 1

Just as with convex lenses, for concave mirrors 1/F = 1/L1 + 1/L2.

1. Solving for L2,
L2 = 1/(1/F - 1/L1) = 51.15 cm
Magnification = L2/L1 = 51.15/93
Image is real, inverted

2. Solving for F,
F = (1/(1/L1 + 1/L2) = 6 cm
Magnification = L2/L1 = 13.2/11
Image is real, inverted

Move the pen (L1) to 27 cm, then L2 = 1/(1/F - 1/L1) = 7.71 cm.
Magnification = L2/L1 = 7.71/27
Image is real, inverted

All images in (1) and (2) are real because L1 > F in all cases.