A candle is placed 14 cm in front of a concave mirror. The image of the candle is on a sheet of paper that is exactly 21 cm in front of the mirror. What is the magnification of the image? What is the focal length of this mirror?

1 Answer
Pallu
Sep 29, 2017

#M = -1 .5#
and
#f= 8 .4# cm

Explanation:

The radius of curvature #R# and the focal length #f# are to be taken as positive for a concave mirror.

Object distance #do = 14 cm #

Image distance #di = 21 cm#

As the image is on the same side of the object, #di# is to be taken positive.

Mirror formula :

#1/(di) + 1/(do) = 1/f#

#1/21 + 1/14 = 1/f#

# (2+3)/42 = 1/f#

# 5/42 =1/f#

#f = 42/5#

# f =8.4 # cm ---------focal length of the mirror.

Magnification formula in terms of object distance and image distance is given as:

#M = - (di)/(do)#

#M = - 21/14#

#M = - 3/2#

# M = - 1.5#
That means the image is real, inverted and enlarged.

enter image source here

When the object is located between C and F, the image will be located beyond C.

In this case, the image is inverted (i.e., the right side up object results in an upside-down image).

The image dimensions are larger than the object dimensions as the absolute value of the magnification is greater than 1.

Finally, the image is a real image. Light rays actually converge at the image location. So the image of the object can be projected upon the sheet of paper.

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