A lamp which is 10.5 cm tall is in front of a concave mirror which has a focal l

Question

A lamp which is 10.5 cm tall is in front of a concave mirror which has a focal length of 45.0 cm.
(a) How tall is the lamp's image if the lamp is a distance of 4.5 cm from the mirror (include sign if negative)?
cm
(b) How tall is the lamp's image if the lamp is a distance of 63.0 cm from the mirror (include sign if negative)?
cm
(c) How tall is the lamp's image if the lamp is a distance of 175.5 cm from the mirror (include sign if negative)?
cm
(d) When a concave mirror forms a real image, is the image always enlarged?

Explanation / Answer

f = 45 cm

y = 10.5 cm (object height)

a)
u = 4.5 cm (object distance)

we know,
1/u + 1/v = 1/f
1/v = 1/f - 1/u

1/v = 1/45 - 1/4.5

==> v = -5 cm (image distance)

m = -v/u = y'/y

y' = y*(-v/u)

= 10.5*(5/4.5)

   = 11.67 cm (image height)
b)
u = 63 cm (object distance)

we know,
1/u + 1/v = 1/f
1/v = 1/f - 1/u

1/v = 1/45 - 1/63

==> v = 157.5 cm (image distance)

m = -v/u = y'/y

y' = y*(-v/u)

= 10.5*(-157.5/4.5)

   = -367.5 cm (image height)
c)
u = 175.5 cm (object distance)

we know,
1/u + 1/v = 1/f
1/v = 1/f - 1/u

1/v = 1/45 - 1/175.5

==> v = 60.52 cm (image distance)

m = -v/u = y'/y

y' = y*(-v/u)

= 10.5*(-60.52/4.5)

   = -141.2 (image height)
d)

no

e) at 2*f

f)

farther from the mirror

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