Question

- Consider a camera that uses a lens with a focal length of 35 mm. How far behind the lens must the film be in order to take a picture of a flower that is 75 cm in front of the lens? - A convex lens is used to make an image of a 10 cm tall arrow on a screen. The arrow sits 25 cm in front of the lens and the image that it creates is 20 mm tall. What is the focal length of the lens?

Answer 1

1.

Given the focal length, $f=35mm$

Object distance, $o=75cm=750mm$

Use formula $\frac{1}{f}=\frac{1}{o}+\frac{1}{i}$

$\frac{1}{35mm}=\frac{1}{750mm}+\frac{1}{i}$

$\frac{1}{35}-\frac{1}{750}=\frac{1}{i}$

$\frac{750-35}{35*750}=\frac{1}{i}$

$\frac{715}{35*750}=\frac{1}{i}$

$\frac{35*750}{715}=i$

ANSWER: ${\color{Red} i=36.7mm}$

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2.

Object distance, $o=25cm$

Object height, $h_{o}=10cm$

Image height, $h_{i}=-20mm=-2cm$

A convex lens is used and the image formed will be inverted so put a negative sign

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Magnification, $M=\frac{h_{i}}{h_{o}}=-\frac{i}{o}$

$\frac{h_{i}}{h_{o}}=-\frac{i}{o}$

$-\frac{2cm}{10cm}=-\frac{i}{25cm}$

$\frac{2}{10}*25=i$

${\color{Red} i=5cm}$

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Use formula $\frac{1}{f}=\frac{1}{o}+\frac{1}{i}$

$\frac{1}{f}=\frac{1}{25cm}+\frac{1}{5cm}$

$\frac{1}{f}=\frac{1}{25}+\frac{1}{5}=\frac{1}{25}+\frac{5}{25}=\frac{6}{25}$

$f=\frac{25}{6}$

ANSWER: ${\color{Red} f=4.167cm}$

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