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 55.0 cm.
(a) How tall is the lamp's image if the lamp is a distance of 44.0 cm from the mirror (include sign if negative)?
     cm
(b) How tall is the lamp's image if the lamp is a distance of 99.0 cm from the mirror (include sign if negative)?
     cm
(c) How tall is the lamp's image if the lamp is a distance of 176.0 cm from the mirror (include sign if negative)?
     cm
(d) When a concave mirror forms a real image, is the image always enlarged?

(e) In general, for a concave mirror with focal length, +f, how far should an object be placed from the mirror to form a real image which is neither enlarged nor reduced (enter your answer as a multiple of f)?
     f

(f) If you want the real image to be reduced, should the object be closer to the mirror than the distance found in (e) or farther from the mirror? closer to the mirror farther from the mirror   

I want how to do it and THE ANSWER.

Explanation / Answer

u1 = 44 cm .....f =+ 55cm....u2 =99cm.........u3 =176cm


a) (1/u1)+(1/v1) = 1/f

v = u*f/(u-f) = -220 cm

I/O = -v1/u1===========> I = 52.5 cm


b) (1/u2)+(1/v2) = 1/f

v2 = u2*f/(u2-f) = +123.75cm
I/O = -v2/u2 = -1.25=========> I = -13.125 cm

c) (1/u3)+(1/v3) = 1/f

v3 = u3*f/(u3-f) =+80 cm
I/O = -v3/u3 = -0.45=========> I = -4.725 cm


e) m= 1.========> v=u

(1/u)+(1/u) =1/f===========>u = 2f

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