Answer to Question #2855 in Optics for cait

Question

The sun falls on a concave mirror and forms an image 3cm from the mirror. If an object 24 mm high is placed 12cm from the mirror, where will its image be formed? Construct the ray diagram. How high is the image? Find the magnification of the mirror.

Answer 1

The Sun forms its image in the focus of the mirror, so F = 3 cm. By the formula:
1/F = 1/D1 + 1/D2/ where F = 3 cm, D1 = 12 cm, we can find the position of the image:
D2 = FD1/(D1-F) =3*12/(12-3) = 4 cm
Te magnification of the mirror is
m = -D2/D1 = -4/12 = -1/3,
therefore the height of the mirror would be H2 = m H1 = -1/3 0.24[cm] = -0.08 [cm] (image is inverted)