Question

A tourist takes a picture of a mountain 21 km away using a camera that has a lens with a focal length of 50 mm. She then takes a second picture when she is only 4.3 km away. What is the ratio of the height of the mountain’s image on the camera’s image sensor for the second picture to its height on the image sensor for the first picture?

Answer 1

in the firct case,

Let u1 = 21 m (object distance)

V1 = v (image distance)

let h is the height of mountain.

magnification, m1 = -v1/u1

image height, h1 = m1*oject height

h1 = (-v1/u1)*h

in the second case,

Let u2 = 4.3 m (object distance)

V2 = v (image distance)

let h is the height of mountain.

magnification, m1 = -v2/u2

image height, h2 = m1*oject height

h2 = (-v2/u2)*h

so, h2/h1 = (-v2/u2)*h/(-v1/u1)*h

= u1/u2

= 21/4.3

= 4.88 <<<<<<<<-----------Answer