Question

The focal length of a camera is 20 cm. Find how far away from the film must be the lens set in order to photograph an object located at a distance 100 cm from the lens.​

Answer 1

$\large\underline{ \sf{Information \: given \: to \: us:-}}$

$\star \:\mathrm{focal \: length \:of \: camera \: = \: 20cm }$

$\star \: \mathrm{ Distance \: of \: object \: from \: lens \: = \: 100cm}$

$\large\underline{ \sf{Need \: to \: calculate:-}}$

$\star \: \mathrm{ Distance \: of \: image \: ? }$

$\large\underline{ \sf{Required \: calculations:-}}$

Here we have been provided with the values of focal length and distance of object. Thus we have been asked to calculate the distance of image, which would be calculated by lens formula.

${\bf{ : \large{\longmapsto}} } \: \boxed{ \bf \frac{1}{v} \: - \: \frac{1}{u} \: = \: \frac{1}{f} }$

$\mathrm{ \bf{Where,}}$

• $\leadsto \: \mathrm{distance \: of \: object \: is \: denoted \: by \: u}$
• $\leadsto \: \mathrm{distance \: of \: image \: is \: denoted \: by \: v}$
• $\leadsto \: \mathrm{focal \: length \: is \: denoted \: by \: f}$

Always remember that focal length is always positive whereas, focal length is in negative.

Formula can be rewritten as,

${\bf{ : \large{\longmapsto}} } \: \boxed{ \bf \frac{1}{v} \: = \: \frac{1}{u} \: + \: \frac{1}{f} }$

Substituting values,

${\bf{ : \large{\longmapsto}} } \:{ \ \sf{ \dfrac{1}{v} \: = \: \dfrac{1}{ - 100} \: + \: \dfrac{1}{20}} }</p><p>$

${\bf{ : \large{\longmapsto}} } \:{ \ \sf{ \dfrac{1}{v} \: = \: \dfrac{1}{25} } }$

We gets,

${\bf{ : \large{\longmapsto}} } \:{ \ \boxed{ \sf{ v \: = \: 25 } }}$

Thus, lens should be setted at a distance of 25 cm .

Answer 2

$\Large{\bf{\green{\mathfrak{\dag{\underline{\underline{Given:-}}}}}}}$

• The focal length of a camera lens is 20 cm .

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{To \: Find:-}}}}}}}$

• How far away from the film must the lens be set in order to photograph an object located at a distance of 100 cm from the lens ?

$\Large{\bf{\red{\mathfrak{\dag{\underline{\underline{Solution:-}}}}}}}$

we have given that focal length is 20 cm, and u as 100 cm.

By using the lens formula

$\pink{\bigstar}$ $\small\underline{\boxed{\bf\green{ \dfrac{1}{v} = \dfrac{1}{u} + \dfrac{1}{f} }}}$

Now we have to substitute the values.

$\\ \longrightarrow\:\bf \purple{\dfrac{1}{v} = \dfrac{1}{ - 100} + \:\dfrac{1}{20} }$

${\bf{ : \large{\longmapsto}} } \:{ \ \sf{ \dfrac{1}{v} \: = \: \dfrac{1}{25} } }$

• Therefore, the lens must be settled in a distance of 25cm