Derive the relation between linear and longitudinal magnification

Asked by sanskrutisahu300 | 12th Jan, 2020, 11:26: AM

Expert Answer:

Magnification, in optics, the size of an image relative to the size of the object creating it.
Linear (sometimes called lateral or transverse) magnification refers to the ratio of image length to
object length measured in planes that are perpendicular to the optical axis.
Longitudinal magnification denotes the factor by which an image increases in size,
as measured along the optical axis.
Linear magnification m = I/O = -v/u  
where I and O are size of image and object respectively.
v and u are mirror-to-image distance and mirror-to-object distance respectively
Longitudinal magnification ml = I/O = -(v2 - v1) / (u2 - u1
By using the mirror equation,  (1/v1 ) + (1/u1 ) = (1/v2 ) + (1/u2 ) = 1/f  ,
we get  , ml = -(v2 - v1) / (u2 - u1) = (v1v2)/(u1u2) = m2

Answered by Thiyagarajan K | 12th Jan, 2020, 12:49: PM

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