Question

Let the transverse magnification produced by a spherical mirror is \[m\]. Then for the same position of objective mirror the longitudinal magnification will be:
A. \[m\]
B. \[\sqrt m \]
C. \[{m^2}\]
D. \[\dfrac{1}{m}\]

Answer 1

Hint As we know lateral or transverse magnification are same and is given as \[m\]and we know the formula to calculate the longitudinal magnification and can be calculated through \[{m_{longitud}} = {\left( {{m_{trans}}} \right)^2}\].

Complete step by step answer As we know we are given as transverse magnification as, \[{m_{trans}} = m\]
And to calculate the longitudinal magnification as, \[{m_{longitud}} = {\left( {{m_{trans}}} \right)^2}\]
By substituting the transverse in formula we get, \[{m_{longitud}} = {m^2}\]
Therefore we get as \[{m^2}\]the longitudinal magnification.

Additional information Lateral magnification is referred to relative heights of objects to height of image in our ray tracings. Through transverse magnification we can calculate the ratio of heights of object and image and we can also calculate the velocities of both the image and object. And transverse magnification changes along optical axes whereas longitudinal magnification is not linear and 3D image is distorted through longitudinal magnification. The word "lateral" is appended above because it only applies to the dimensions of the objects perpendicular to the optical axis. As stated above, this is almost exclusively what we will be working with, let's take a moment to look at magnification in the cases of the plane reflector when the object arrow is parallel to the optical axis.

Note As we know about lateral magnification its formula is \[m = - \dfrac{v}{u}\], here we have negative sign but we always choose its magnitude but if we have negative sign in option then we have to take care of this negative sign and take signed value of velocities that is with direction. And the same is in the case of longitudinal magnification.