Question

The image obtained with a convex lens is erect and its length is 4 times the length of object in the focal length of the lens is 20 cm. Calculate the object and image distances.

Mention Any Two Uses of Convex lens.
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Answer 1

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

$\Large\bold{\boxed{\boxed{15\:cm }}}$

$\rule{200}{4}$

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

For a Convex lens : erect image⇒positive magnification

$\tt\bold{m=\frac{h_I}{h_0}=\frac{v}{u}=4}$

Cross-multiplying

$\tt\bold{\Rightarrow\:v=4u}$

By Using Lens Formula :

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

Given that :

Focal length (f) = 20 cm

Object distance = - u

$\bf\bold{\Rightarrow\:-\frac{1}{4u}-\frac{1}{-u}=\frac{1}{20}}$

$\bf\bold{\Rightarrow\frac{3}{4u}=\frac{1}{20}}$

$\bf\bold{\Rightarrow\:u= 15\:cm}$

Hence, the distance of object from lens is 15 cm

____________________________

Uses of Convex lens:

• In spectacles for eyes suffering from hypermetropia.
• In the lens combination of camera, telescope, microscope.

Answer 2

Solution:

Given:

=> Magnification = +4

=> Focal length = 20 cm.

To find:

=> Object distance (u)

=> Image distance (v)

formula used:

$\sf{\implies \dfrac{1}{f}=\dfrac{1}{v}=\dfrac{1}{u}}$

So,we know that

$\sf{\implies Magnification = \dfrac{v}{u}}$

$\sf{\implies v = 4u}$

By using lens formula,

$\sf{\implies \dfrac{1}{f}=\dfrac{1}{v}=\dfrac{1}{u}}$

$\sf{\implies \dfrac{1}{20} = \dfrac{1}{4u} - \dfrac{1}{u}}$

$\sf{\implies \dfrac{1}{20} =\dfrac{1-4}{4u}}$

$\sf{\implies \dfrac{1}{20} = -\dfrac{3}{4u}}$

$\sf{\implies 4u = -60}$

$\sf{\implies u = -\dfrac{60}{4}}$

${\boxed{\boxed{\sf{\implies u = -15\;cm}}}}$

So,

=> v = 4u

=> v = 4 × (-15)

=> v = -60 cm.

Hence,

Object distance = -15 cm.

Image distance = -60 cm.

Uses of convex lens:

• Convex lens is used as a magnifying glass.
• Convex lens are used in binoculars which are used to observe the things at few meters away from the observer.