Problem 24.05 A concave spherical mirror has a radius of curvature of 14.0 cm .

Question

Problem 24.05

A concave spherical mirror has a radius of curvature of 14.0 cm .

Part A

Calculate the location of the image formed by an 15.0-mm-tall object whose distance from the mirror is 28.0 cm .

9.33

Correct

Part B

Calculate the size of the image.

5.00

Correct

Part C

Calculate the location of the image formed by an 15.0-mm-tall object whose distance from the mirror is 14.0 cm .

14.0

Part D

Calculate the size of the image.

15.0

Correct

Part E

Calculate the location of the image formed by an 15.0-mm-tall object whose distance from the mirror is 3.50 cm .

-7.00

Correct

Part F

Calculate the size of the image.

30.0

Correct

Part G

Calculate the location of the image formed by an 15.0-mm-tall object whose distance from the mirror is 10.0 m .

Part H

Calculate the size of the image.

9.33

Explanation / Answer

A) focal length, f1 = R/2 = 14/2 = 7 cm

object distance, s = 28 cm

Apply, 1/s1 + 1/s1' = 1/f

1/s1' = 1/f - 1/s1

1/s1' = 1/7 - 1/28

s1' = 9.33 cm <<<<<<---------Answer

B) magnificationm, m = -s1'/s1

= -9.33/28

= -0.333

magnification, m = image height/object height

= y'/y

y' = m*y

= -0.333*15 mm

= -5 mm (here negative sign indicates image is inverted)

C)

1/s2' = 1/f - 1/s2

1/s2' = 1/7 - 1/14

s2' = 14 cm

D) magnificationm, m = -s2'/s2

= -14/14

= -1

magnification, m = image height/object height

= y'/y

y' = m*y

= -1*15 mm

= -15 mm (here negative sign indicates image is inverted)

E)
1/s3' = 1/f - 1/s3

1/s3' = 1/7 - 1/3.5

s3' = -7 cm <<<<<<---------Answer

F) magnificationm, m = -s3'/s3

= -(-7)/3.5

= 2

magnification, m = image height/object height

= y'/y

y' = m*y

= 2*15 mm

= +30 mm (here POSItive sign indicates image is UPRIGHT)

g)

1/s4' = 1/f - 1/s4

1/s4' = 1/7 - 1/1000

s3' = 7.05 cm <<<<<<---------Answer

h) magnificationm, m = -s4'/s4

= -7.05/1000

= -7.05*10^-3

magnification, m = image height/object height

= y'/y

y' = m*y

= -7.05*10^-3*15 mm

= -0.105 mm (here negative sign indicates image is inverted)

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