Question

The image obtained with a convex lens is erect and its length is 8 times the length of object in the focal length of the lens is 16 cm. Calculate the object and image distances.
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Answer 1

$\Large\bold{\underline{\underline{Answer:-}}}$

$\Large\bold{\boxed{\boxed{14\:cm }}}$

$\rule{200}{4}$

$\bf\small\bold{\underline{\underline{Step-By-Step\:Explanation:-}}}$

For a Convex lens : erect image⇒positive magnification

$\tt\bold{m=\frac{h_I}{h_0}=\frac{v}{u}=8}$

Cross-multiplying

$\tt\bold{\Rightarrow\:v=8u}$

By Using Lens Formula :

$\bf\Large\boxed{\frac{1}{v}-\frac{1}{u}=\frac{1}{f}}$

Given that :

Focal length (f) = 16 cm

Object distance = - u

$\bf\bold{\Rightarrow\:-\frac{1}{8u}-\frac{1}{-u}=\frac{1}{16}}$

$\bf\bold{\Rightarrow\frac{7}{8u}=\frac{1}{16}}$

$\bf\bold{\Rightarrow\:u= 14 \:cm}$

Hence, the distance of object from lens is 14 cm

Answer 2

Answer:

${\bold{\therefore Object \: distance = 14 \: cm}}$

${\bold{\therefore Image\: distance = 112\: cm}}$

$\huge{\bold{\underline{\underline{SOLUTION-}}}}$

• In the given question information given about a convex lens and its magnification and focal length is given.

• We have to find the object and image distance.

$\underline \bold{Given : } \\ \implies Focal \: length(f) = 16 \: cm \\ \\\implies Magnification=8\\ \\ \underline \bold{To \: Find : } \\ \implies Object \: distance(u) = ? \\ \\ \implies Image \: distance(v) = ?$

• According to given question :

$\bold{For \: convex \: lens : } \\ \implies Magnification = \frac{v}{u} \\ \\ \implies 8 = \frac{v}{u} \\ \\ \implies v = 8u \\ \\ \bold{Using \: lens \: formula : } \\ \implies \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \\ \\ \implies \frac{1}{16} = \frac{1}{8u} - \frac{1}{ - u} \\ \\ \implies \frac{1}{16} = \frac{1}{8u} + \frac{1}{u} \\ \\ \implies \frac{1}{16} = \frac{7}{8u} \\ \\ \implies 8u = 16 \times 7 \\ \\ \implies u = \frac{ \cancel{16} \times 7}{ \cancel8} \\ \\ \bold{\implies u = 14 \: cm} \\ \\ \bold{\implies v = 8 \times 14 = 112 \: cm} \\ \\ \bold{\therefore Object \: distance = 14 \: cm} \\ \bold{\therefore Image \: distance = 112 \: cm}$