150k views
2 votes
A 35-mm single lens reflex (SLR) digital camera is using a lens of focal length 35.0 mm to photograph a person who is 1.80 m tall and located 3.60 m from the lens. (a) How far is the CCD sensor from the lens when the person is in focus?

(b) How tall is the person's image on the CCD sensor?

1 Answer

3 votes

Answer:

a) 35.44 mm

b) 17.67 mm

Step-by-step explanation:

u = Object distance = 3.6 m

v = Image distance

f = Focal length = 35 mm


h_u= Object height = 1.8 m

a) Lens Equation


(1)/(f)=(1)/(u)+(1)/(v)\\\Rightarrow (1)/(f)-(1)/(u)=(1)/(v)\\\Rightarrow (1)/(v)=(1)/(35)-(1)/(3600)\\\Rightarrow (1)/(v)=(713)/(25200) \\\Rightarrow v=(25200)/(713)=35.34\ mm

The CCD sensor is 35.34 mm from the lens

b) Magnification


m=-(v)/(u)\\\Rightarrow m=-(35.34)/(3600)


m=(h_v)/(h_u)\\\Rightarrow -(35.34)/(3600)=(h_v)/(1800)\\\Rightarrow h_v=-(35.34)/(3600)* 1800=-17.67\ mm

The person appears 17.67 mm tall on the sensor

User Stefan Wuebbe
by
8.5k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.