Question

A camera phone called the iPhone X has an image sensor size of 5 mm and a focal length of 4 mm. How long of a selfie-stick must you use to take a picture of you and Liz Cambage of the Las Vegas Aces who stands at 2.032 meters and not be cropped (i.e., the image size can't exceed 5 mm)?

Answer 1

length of selfie-stick is 1.62 m

Step-by-step explanation:

Given data

image size h1 = 5 mm = 5 ×
`10^(-3)` m

focal length = 4 mm = 4 ×
`10^(-3)` m

distance h2 = 2.032 m

to find out

How long of a selfie-stick

solution

here we find first magnification

that is M = h1 /h2

M = 5 ×
`10^(-3)` / 2.032

M = 2.46 ×
`10^(-3)`

and we know M = p/q

so p = Mq = 2.46 ×
`10^(-3)` q

so we apply lens formula

1/f = 1/p - 1/q

1/ 4 ×
`10^(-3)` = 1 / 2.46 ×
`10^(-3)` q - 1/q

q = 1.622 m

so length of selfie-stick is 1.62 m