Question

4. My camera has a sensor that is 23 x 15 mm. Like every tourist, I would like to take a picture of the Washington Square Arch, which is 23 meters tall. If I want to take a picture lengthwise, this means the image of the Arch must be 23 mm tall (1/1000 of the size of the object). a) For the following focal length lenses, f = 20,40,80, how far should the lens be from the Arch, and how far from the sensor? b) If, like every tourist, I now want to take a picture of the Empire State Building, which is located 2 km, how much do I need to move each lens, and in which direction? C) The Empire state building is 443 meters tall. Given the previous information in the problem, which lens should I choose to take a picture of the Empire State Building from Washington Square Park?

Answer 1

a) magnification m = -I/O = 1/1000

I - image distance

O - object distance

O = -1000 I

using lens formula

1/I -1/O =1/f

I = 1.001 f

for f= 20 mm

image distance I = 20.02 mm

object distance O = 1000 I = 20.02 m

f= 40 mm

I = 40.04 mm

O = 40.04 m

f= 80mm

I = 80.08 mm

O = 80.08 m

b) Object distance O = 2km

the object is at infinity , image is formed at focus.

The lens has to be set at 20.40,80 mm from the sensor.

c) magnification m = I/O

image forms at focus i.e. I= f

m = f/O , O is fixed, to get best magnification use the lens with highest f i.e 80 mm