Question

The radius of curvature of a spherical convex mirror is 22 cm. Describe the image formed when a 15-om-tall object is positioned at various 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) 20 cm from the mirror d 24.4 x cm e real virtual Orientation of the image: upright s inverted (b) 22 cm from the mirror di 11 e real o virtual Orientation of the image: o upright s inverted (e) 100 em from the mirror di 165 hl = 12.35 rcal o virtual Orientation of the image o upright inverted

Answer 1

a)

f = focal length = - 22 cm

h_o = object height = 15 cm

h_i = image height = ?

d_o = object distance = 20 cm

d_i = image distance = ?

using the mirror equation

1/d_i + 1/d_o = 1/f

1/d_i + 1/20 = 1/(-22)

d_i = - 10.5 cm

using the equation

h_i/h_o = - d_i/d_o

h_i/15 = - (- 10.5)/20

h_i = 7.875 cm

Imgae distance : 10.5 cm

Image height : 7.875 cm

Type of image : Virtual

Orientation : Upright

b)

f = focal length = - 22 cm

h_o = object height = 15 cm

h_i = image height = ?

d_o = object distance = 22 cm

d_i = image distance = ?

using the mirror equation

1/d_i + 1/d_o = 1/f

1/d_i + 1/22 = 1/(-22)

d_i = - 11 cm

using the equation

h_i/h_o = - d_i/d_o

h_i/15 = - (- 11)/22

h_i  = 7.5 cm

Imgae distance : 11 cm

Image height : 7.5 cm

Type of image : Virtual

Orientation : Upright

c)

f = focal length = - 22 cm

h_o = object height = 15 cm

h_i = image height = ?

d_o = object distance = 100 cm

d_i = image distance = ?

using the mirror equation

1/d_i + 1/d_o = 1/f

1/d_i + 1/100 = 1/(-22)

d_i = - 18.03 cm

using the equation

h_i/h_o = - d_i/d_o

h_i/15 = - (- 18.03)/22

h_i  = 12.3 cm

Imgae distance : 18.03 cm

Image height : 12.3 cm

Type of image : Virtual

Orientation : Upright