a real image three times as large as the object is formed using a concave mirror of radius of curvature 20.0 cm. Find the locations of the object and the image.

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Here, m = -3 (real image),

f = -20/2 = -10 cm (concave mirror).

Applying mirror equation and the magnification equation for concave mirror,

1/f = 1/d_o + 1/d_i

and

m = h_i/h_o = - d_i/d_o

Putting the values, we get

-1/10 = 1/d_o + 1/d_i ---- (i)

and -3 = - d_i/d_o ---- (ii)

or, d_i = 3 d_o

Therefore,

-1/10 = 1/d_o + 1/(3*d_o)

Or, (3+1)/(3d_o) = -1/10

Or, 4/(3d_o) = -1/10

Or, d_o = -40/3 = -13.33 cm (object on the left of the mirror)

d_i = 3*d_o = -40*3/3 = -40 cm (image on the left of the mirror).

Therefore the object was in the front of the image, 13.33 cm away from it, the image was also in the front side, 40 cm away from the concave mirror.

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