Question

An object is 23.5cm from the center of a silvered spherical glass Christmas tree ornament 6.35 cm in diameter. A) What is the position of its image? s'=? B)What is the magnification of its image? m=?

Answer 1

object distance = 23.5 cm

RAdius R = 6.35/2 = 3.175 cm

f = R/2 = 3.175 /2 = 1.5875 cm

a. 1/f = 1/s + 1/s'

1/1.5875 = 1/23.5 + 1/s'

s' = 1.70 cm

b.

m =-s'/s = - 1.70/23.5 = - 0.0723

Answer 2

object distance = 23.5 cm

RAdius R = 6.35/2 = 3.175 cm

f = R/2 = 3.175 /2 = 1.5875 cm

a. 1/f = 1/s + 1/s'

1/1.5875 = 1/23.5 + 1/s'

s' = 1.70 cm

b. m =- 1.70/23.5 = 0.0723

Answer 3

focus length is - r/2 = - 6.35/4= - 1.5875 cm (negative because behind the mirror)

now use
1/f = 1/do + 1/di
1/- 1.5875 = 1/23.5 + 1/di
di = - 1.487 cm = image distance (negative, because di is behind the mirror. )
the image is virtual and upright.
--
the magnification m = id di/do = (-) 1.487/ 23.5 = (-) 0.06328

Answer 4

Radius R = D/2 = 6.35/2   = 3.175 cm

object disdtant u = 23.5 cm

also f = 2R = 6.35 cm

apply 1/f = 1/u +1/v

v = uf/(u-f)

v = 6.35* 23.5/(23.5-6.35)

v = 8.701 cm is the image location

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magnifictaion m = -v/u

m = 8.701/23.5

m = 0.370 is the magnification

Answer 5

Focus length is - r/2 =-diameter/4= - 6.35/4= - 1.5875 cm (negative because behind the mirror)

now use
1/f = 1/do + 1/di
1/- 1.5875 = 1/23.5 + 1/di
di = - 1.487 cm = image distance (negative, because di is behind the mirror. )
the image is virtual and upright.
--
the magnification m = di/do = (-) 1.487/ 23.5 = (-) 0.06328 (negative because object is vertically downward)

Answer 6