Question

In a pair of overlapping vertical photographs, the mean distance between the principal points is $95.90mm$. At the time of photography, the aircraft was $3000m$ above the terrain which was at datum level and the camera had a focal length of $250mm$. A tower was observed and the difference in parallax measurements of its top and base was found to be $3.50mm$. The height of the tower, the base of which is also at datum level, will be

• A. $105.05m$
• B. $115.04m$
• C. $95m$
• D. $112.45m$

Answer 1

The correct option is A $105.05m$

$S=\text{Scale of photograph, for datum elevation}$

$=\frac{f}{H}=\frac{250}{3000\times 1000}=\frac{1}{12000}$

$or1cm=120m$

$\text{For the datum elevation,}$

$\frac{B}{b}=\frac{H}{f}$
$\Rightarrow B=\frac{H}{f}\times b$

$\frac{1}{S}\times b=12000\times \frac{95.50}{1000}$

$=1146m$

$\therefore \text{Parallax,}{P}_{bottom}=\frac{Bf}{H-f}=\frac{1146\times 250}{(3000-0)}=95.5mm$

$P_{top}=95.5+3.5=99mm$

$\therefore$ $P_{top}=\frac{1146\times 250}{3000-h}=99$

$\therefore h=106.06mm$