The radius of curvature of a spherical convex mirror is 15 cm. Describe the imag

Question

The radius of curvature of a spherical convex mirror is 15 cm. Describe the image formed when a 20-cm-tall object is positioned at the the following distances. For each case, provide the image distance, the image height, the type of image (real or virtual), and the orientation of the image (upright or inverted).

(a) 5 cm from the mirror cm cm O The image is virtual and inverted ) The image is virtual and upright. O The image is real and upright. The image is real and inverted The image is real and inverted (b) 20 cm from the mirror cm cm The image is virtual and inverted O The image is virtual and upright. O The image is real and upright The image is real and inverted (c) 100 cm from the mirror dl =-8.1 cm =-1.62 cm O The image is virtual and inverted O The image is virtual and upright. O The image is real and upright The image is real and inverted

Explanation / Answer

take the object side distances as negative and the other side as positive.

focal length of mirror = +15/2 = +7.5 cm,, ho = 20 cm

use 1/f = 1/v + 1/u v = dI , u = do

a) 2/15 = 1/v - 1/5

v = 3 cm hI = (3/5) x 20 = 12 cm virtual , upright

b) 2/15 = 1/v - 1/20

v = 60/11 = 5.454 cm hI = (60/11) x 20/20 = 5.454 cm virtual, upright

c) 2/15 = 1/v - 1/100   

v = 300/43 = 6.976 cm hI = 6.976 x 20/100 = 1.395 cm virtual upright

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