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  4. A photographic camera with a lens of focal length 5 cm is used for capturing images. The vertical length of the film used is 24 mm in which image of a 1.68 m tall man is to be captured. Find the minimum distance (in cm ) of the man from the lens such that his complete image can be obtained.

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Q. A photographic camera with a lens of focal length $5\,cm$ is used for capturing images. The vertical length of the film used is $24\,mm$ in which image of a $1.68\,m$ tall man is to be captured. Find the minimum distance (in $cm$ ) of the man from the lens such that his complete image can be obtained.

NTA AbhyasNTA Abhyas 2022Ray Optics and Optical Instruments

Solution:

The lens of the camera is convex and the image is inverted
$m=\frac{h_{i}}{h_{o}}=-\frac{24 m m}{1.68 m}=-\frac{1}{70}$
$m=\frac{f}{f + u}=-\frac{1}{70}$
$70f=-f-u$
$-u=71f=355\,cm=3.55\,m$