A movie camera with a lens of focal length 75 mm takes a picture of a 180 cm tall person standing 25 m away. What is the height of the image of the person on the film? (Assume the distance of the person from camera to be very large as compared to its focal length)

2.7 mm

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5.4 mm

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10.8 mm

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16.2 mm

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Solution

The correct option is B 5.4 mm
Let us consider the person as the object. So,

Object position (u) = Distance of person from the camera = 25 m

Size of the person = Object size $(h_{o})$
= 180 cm = 1.8 m

Since 25 m (Position of person) >> 0.075 m (focus of the lens), rays from the person can be assumed to be parallel.

Image of the person will be formed in the camera film on the focus.
Image position (v) = 0.075 m (Focal length given as 75 mm)

To calculate the image size (height of person on the film $h_{i}$ ), we will use the magnification formula.
m = $\frac{v}{u}$ = $\frac{I m a g e s i z e (h i)}{O b j e c t s i z e (h o)}$

Placing values of v, u and $h_{o}$ ,
$\Rightarrow$ $\frac{0.075}{25}$ = $\frac{h i}{1.8 m}$
$\Rightarrow$ $h_{i}$ = 0.003 x 1.8 = 0.0054 m
= 5.4 mm
So, the height of the person on the film will be 5.4 mm.

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A movie camera with a lens of focal length 75 mm takes a picture of a 180 cm tall person standing 25 m away. What is the height of the image of the person on the film? (Assume the distance of the person from camera to be very large as compared to its focal length)​

A movie camera with a lens of focal length 75 mm takes a picture of a 180 cm tall person standing 25 m away. What is the height of the image of the person on the film? (Assume the distance of the person from camera to be very large as compared to its focal length)