Answer:
a) 35.44 mm
b) 17.67 mm
Explanation:
u = Object distance = 3.6 m
v = Image distance
f = Focal length = 35 mm
[tex]h_u[/tex]= Object height = 1.8 m
a) Lens Equation
[tex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\\\Rightarrow \frac{1}{f}-\frac{1}{u}=\frac{1}{v}\\\Rightarrow \frac{1}{v}=\frac{1}{35}-\frac{1}{3600}\\\Rightarrow \frac{1}{v}=\frac{713}{25200} \\\Rightarrow v=\frac{25200}{713}=35.34\ mm[/tex]
The CCD sensor is 35.34 mm from the lens
b) Magnification
[tex]m=-\frac{v}{u}\\\Rightarrow m=-\frac{35.34}{3600}[/tex]
[tex]m=\frac{h_v}{h_u}\\\Rightarrow -\frac{35.34}{3600}=\frac{h_v}{1800}\\\Rightarrow h_v=-\frac{35.34}{3600}\times 1800=-17.67\ mm[/tex]
The person appears 17.67 mm tall on the sensor
