Here is the question as given in my textbook:
Find the distance of the object from a concave mirror of focal length 10 cm so that the image size is 4 times the size of the object.
The solution in my textbook has the following data stated:
$u=-x$ as it is assumed that the object is real.
$v=-4x$ as it is assumed in case 1 that a real image will be formed and $|\frac{v}{u}|=|m|=4$
So now I am not able to understand why the image distance $v$ is taken $-4x$. In the question it is given that the object size is magnified 4 times, and not the distance of the of the object from the mirror.
And the magnification formula is $\frac{-v}{u}=m$, so why does the solution include the modulus of the formula?
Am I missing something in analysing the solution?
Best Answer
$u$ is the distance of the object to the reflecting/refracting surface. $v$ is the distance from that surface to the image.
by convention
knowing these rules is paramount to properly understanding optics problems as they are posed.
in this question the magnifcation is given as 4, whereas information on orientation is unknown.therefore the sign of $v$ is unknown (i am assuming there was no diagram that came along with the question). since u is assigned a negative value $-x$, then $v$ must also be a negative value if the image is real (now the information is given to you). this is interpreted as both object and image being on the same side of the mirror, on the x axis. proper use of the formula $m=\frac{-v}{u}$ will yield a negative value for m, indicating an inverted image relative to the object. in fact it is implicit from the rules above that for concave mirrors, real images are always inverted--an upright image must be a virtual image.