Question

A movie star catches a paparazzi reporter snapping pictures of her at home and claims that he was trespassing. He, of course denies the allegations. To prove her point, she submits as evidence the film that she confiscated. Her height of 1.75 m appears as an 8.25 mm high image on the film. Additionally, she submits that the camera that was used has a focal length of 210 mm. How far away was the reporter when he took the picture? (All the information that is given).

Answer 1

44.755 m

Step-by-step explanation:

Given:

Height of the movie star, H = 1.75 m = 1750 mm

Height of the image, h = - 8.25 mm

Focal length of the camera = 210 mm

Let the distance of the object i.e the distance between camera and the movie star be 'u'

and

distance between the camera focus and image be 'v'

thus,

magnification, m =
`\frac{\textup{h}}{\textup{H}}`

also,

m =
`\frac{\textup{-v}}{\textup{u}}`

thus,

`\frac{\textup{-v}}{\textup{u}}=\frac{\textup{h}}{\textup{H}}`

or

`\frac{\textup{-v}}{\textup{u}}=\frac{\textup{-8.25}}{\textup{1750}}`

or

`\frac{\textup{1}}{\textup{v}}=-\frac{\textup{1750}}{\textup{-8.25}}*\frac{1}{\textup{u}}` ....................(1)

now, from the lens formula

`\frac{\textup{1}}{\textup{f}}=\frac{\textup{1}}{\textup{u}}+\frac{1}{\textup{v}}`

on substituting value from (1)

`\frac{\textup{1}}{\textup{210}}=\frac{\textup{1}}{\textup{u}}+-\frac{\textup{1750}}{\textup{-8.25}}*\frac{1}{\textup{u}}`

or

`\frac{\textup{1}}{\textup{210}}=\frac{\textup{1}}{\textup{u}}(1 -\frac{\textup{1750}}{\textup{-8.25}})`

or

u = 210 × ( 1 + 212.12 )

or

u = 44755.45 mm

or

u = 44.755 m