Question

You wish to produce inverted real images of an object with the given magnification using a converging mirror. How far from the mirror must you place the object in each case (express your answer in terms of the focal length of the mirror)? M = -0.5 M = -1 M = -2 M = -4

Answer 1

Let f be the focal length, o be the object dist and i be the image dist.

from the defination of magnification,

M = -i/o

a)M = -i/o = -0.5

i = 0.5o

from lens eqn, 1/f = 1/i + 1/o

1/f = 1/0.5o + 1/o = 1/o(1/0.5 + 1) = 3/o

o = 3f

b)M = -1 = -i/o => i = o

1/f = 1/o + 1/o = 2/o => o = 2f

o = 2f

c)M = -2 = -i/o =>i = 2o

1/f = 1/2o +1/o = 1/o (1/2 + 1) = 1.5o

o = 3/2f

d)M = -4 = -i/o => i = 4o

1/f = 1/4o + 1/o = 1/o (1/4 + 1) = 5/4o

Mo = 5/4f