Question

A convex spherical mirror has a radius of curvature of 9.60 cm.

A) Calculate the location of the image formed by an 7.65-mm-tall object whose distance from the mirror is 18.0 cm. Answer in cm.

B) Calculate the size of the image. Answer in mm.

C) Calculate the location of the image formed by an 7.65-mm-tall object whose distance from the mirror is 10.0 cm. Answer in cm.

D) Calculate the size of the image. Answer in mm.

E) Calculate the location of the image formed by an 7.65-mm-tall object whose distance from the mirror is 2.50 cm. Answer in cm.

F) Calculate the size of the image. Answer in mm.

G) Calculate the location of the image formed by an 7.65-mm-tall object whose distance from the mirror is 10.2 cm. Answer in cm.

H) Calculate the size of the image. Answer in mm.

Answer 1

given
R = 9.60 cm
for a convex mirror, focal length f = -R/2

= -9.6/2

= -4.80 cm

A) object height, h = 7.65 mm
object distance, u = 18.0 cm
let v is the image distance
use , 1/u + 1/v = 1/f

1/v = 1/f - 1/u
1/v = 1/(-4.8) - 1/18
v = -3.79 cm <<<<<<<<<----------------Answer

B) magnification, m = -v/u = -(-3.79)/18 = 0.2106

imge height, h' = m*object height

= 0.2106*7.65

= 1.61 mm <<<<<<<<<----------------Answer

C)
object distance, u = 10.0 cm
let v is the image distance
use , 1/u + 1/v = 1/f

1/v = 1/f - 1/u
1/v = 1/(-4.8) - 1/10
v = -3.24 cm <<<<<<<<<----------------Answer

D) magnification, m = -v/u = -(-3.24)/10 = 0.324

imge height, h' = m*object height

= 0.324*7.65

= 2.48 mm <<<<<<<<<----------------Answer

E) object distance, u = 2.50 cm
let v is the image distance
use , 1/u + 1/v = 1/f

1/v = 1/f - 1/u
1/v = 1/(-4.8) - 1/2.5
v = -1.64 cm <<<<<<<<<----------------Answer

F) magnification, m = -v/u = -(-1.64)/2.5 = 0.656

imge height, h' = m*object height

= 0.656*7.65

= 5.02 mm <<<<<<<<<----------------Answer

G) object distance, u = 10.2 m = 1020 cm
let v is the image distance
use , 1/u + 1/v = 1/f

1/v = 1/f - 1/u
1/v = 1/(-4.8) - 1/1020
v = -4.78 cm <<<<<<<<<----------------Answer

H) magnification, m = -v/u = -(-4.78)/1020 = 0.004686

image height, h' = m*object height

= 0.004686*7.65

= 0.0358 mm <<<<<<<<<----------------Answer