Question

An installed surveillance in Camella St. uses a concave mirror whose focal length is 6.24m. A crime scene was recorded where the suspect stabbed a man walking on the street. The suspect image distance from the surveillance was 11.3m. The height of the suspect’s image is 0.9m. Make a ray diagram and a sketch of the actual scene

Answer 1

Answer on Question #71036, Physics / Optics

An installed surveillance in Camella St. uses a concave mirror whose focal length is $6.24\mathrm{m}$ . A crime scene was recorded where the suspect stabbed a man walking on the street. The suspect image distance from the surveillance was $11.3\mathrm{m}$ . The height of the suspect's image is $0.9\mathrm{m}$ . Make a ray diagram and a sketch of the actual scene

Solution:

PF is the focal length of concave mirror, PF=f=6.24 m

PA' is image distance, PA'=di=11.3 m

PO=2f=12.48 m

PA is the object distance, PA=d0

AB is the height of the object, AB=H

A'B' is the height of the image, AB=h

The mirror formula in this case:

$$\frac {1}{d _ {0}} + \frac {1}{d _ {i}} = \frac {1}{f} (1)$$ $$\text {O f} (1) \Rightarrow \frac {1}{d _ {0}} = \frac {1}{f} - \frac {1}{d _ {i}} (2)$$ $$\text {O f} (2) \Rightarrow \frac {1}{d _ {0}} = \frac {d _ {i} - f}{f d _ {i}} (3)$$ $$\text {O f} (3) \Rightarrow d _ {0} = \frac {f d _ {i}}{d _ {i} - f} (4)$$ $$\text {O f} (4) \Rightarrow d _ {0} = 1 3. 9 4 \mathrm {m}$$

Magnification of mirror: $k = \frac{d_0}{d_i} = \frac{H}{h}$ (5)

$$\text {O f} (5) \Rightarrow H = \frac {d _ {0}}{d _ {i}} h (6)$$ $$\text {O f} (6) \Rightarrow H = 1. 1 1 m$$

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