If the focal length of a camera is 20cm, the distance from the film at...

If the focal length of a camera is 20cm, the distance from the film at which the lens must be set to produce a sharp image of 100cm away is

Focal length: \( f = 20 \, \text{cm} \)

Object distance: \( u = 100 \, \text{cm} \) (positive since it's in front of the lens)
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Using the lens formula:
\(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\)

Substituting the known values:
\(\frac{1}{20} = \frac{1}{v} + \frac{1}{100}\)

Rearranging to solve for \( v \):
\(\frac{1}{v} = \frac{1}{20} - \frac{1}{100}\)

Finding a common denominator (100):
\(\frac{1}{20} = \frac{5}{100}\)

Thus, \(\frac{1}{v} = \frac{5}{100} - \frac{1}{100} = \frac{4}{100}\)

Solving for \( v \):
\(v = \frac{100}{4}\) = 25 cm

There is an explanation video available below.

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