An object of height y o = + 2 m is placed in front of a concave spherical mirror

Question

An object of height yo = +2 m is placed in front of a concave spherical mirror (focal length of size 1.5 m), at the various locations listed in parts a-c.

a.) When the object is placed 4 m away from the mirror, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

b.) When the object is placed 2.25 m away from the mirror, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

c.) When the object is placed 0.75 m away from the mirror, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

The same object (of height = 2 m) is placed in front of a converging lens (focal length of size 1.5 m), at the various locations listed in parts d-f.

d.) When the object is placed 4 m away from the lens, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

e.) When the object is placed 2.25 m away from the lens, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

f.) When the object is placed 0.75 m away from the lens, please find:
image distance = m
type/orientation of image = ---Select---real and uprightreal and invertedvirtual and uprightvirtual and inverted
magnification =
height of image = m

Explanation / Answer

f = +1.5 m

object height, yo = 2 m


a)
object distance, u = 4 m

1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/1.5 - 1/4

v = 2.4 m

image is real and inverted

magnification, m = y'/yo = | v/u |

y' = yo*(v/u)

= 2*2.4/4

= 1.2 m

b)

object distance, u = 2.25 m

1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/1.5 - 1/2.25

v = 4.5 m


image is real and inverted

magnification, m = y'/yo = | v/u |

y' = yo*(v/u)

= 2*4.5/4

= 2.25 m

c)

object distance, u = 0.75 m

1/u + 1/v = 1/f

1/v = 1/f - 1/u

1/v = 1/1.5 - 1/0.75

v = -1.5 m


image is virtual and upright

magnification, m = y'/yo = | v/u |

y' = yo*(v/u)

= 2*1.5/4

= 0.75 m

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