Assume Vera has a near point focus of 30cm and is given a concave mirror with a

Question

Assume Vera has a near point focus of 30cm and is given a concave mirror with a radius of curvature of 10cm and a converging lens (magnifier) with a focal length of 2cm. She wishes to build a system to magnify a small object. The magnifier is placed to provide maximum magnification for the image created by the mirror. Find the distance that the object and the magnifier must be placed from the mirror to magnify the object by 30x. Is the object viewed by Vera upright or inverted? (please answer this last question!)

Explanation / Answer

for lens here

1/f = -1/u + 1/v

here u = -x, v = -30

f = +2

1/-30 - 1/-x = 1/2

x = 15/8 cm

m2 = V/u = -30/15/8 = 16

m1m2 = 30

m1 = 15/8

for Mirroe Now

1/u + 1/v = 1/f

m1 = 15/8

v = 15/8 u

so

1/(15 y/8) + (-1/y) = 1/-5

y = 7.34 cm (ANSWWR)

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