Question

3. A 5 cm needle is placed 10 cm away from a convex
mirror of focal length 10 cm. Find the location of the
image and the magnification.​

Answer 1

Answer: Hey Buddy!! Here is your answer.

Explanation:

Here, h1=5cm,u=−10cm,

f=40cm

From 1v=1f−1u=140−1−10=540=18

v=8cm

Image is virtual, erect and is formed 8cm behind the mirror.

Magnification, m=h2h1=−vu=−8−10=45

h2=45h1=45×5=4cm

As needle is moved farther away from the mirror, image shifts towards the focus and its size goes on decreasing.

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Answer 2

${\huge{\red{\sf{Given}}}}\begin{cases}\leadsto \bf{Height\:of\:object\:is\:5cm}\\\leadsto \bf{Object\:distance\:is\:10cm}\\\leadsto\bf{Focal\:length \:is\:10cm}\end{cases}$

${\huge{\red{\sf{To\:Find}}}}\begin{cases}\leadsto \bf{Location\:of\:image}\\\leadsto{\bf{Magnification\:produced}}\end{cases}$

$\huge\red{\underline{\bf{\green{Answer}}}}$

We know, whenever in case if a concave lens if the object is at focus then the image is at infinity.

${\red{\underline{\sf{(\mapsto Refer\:to\:ray\:diagram\:in\:attachment)}}}}$

______________________________________

Let's use mirror's formula:

${\underline{\purple{\bf{\hookrightarrow Mirror\:Formula}}}}$

$\large\purple{\boxed{\boxed{\orange{\bf{\mapsto \dfrac{1}{v}+\dfrac{1}{u}=\dfrac{1}{f}}}}}}$

Using this,

$\sf{\implies \dfrac{1}{v}+\dfrac{-1}{10cm}=\dfrac{1}{-10cm}}$

$\sf{\implies \dfrac{1}{v}=\dfrac{1}{10cm}-\dfrac{1}{10cm}}$

$\sf{\implies \dfrac{1}{v}=\cancel{\dfrac{1}{10cm}}-\cancel{\dfrac{1}{10cm}}}$

$\sf{\implies \dfrac{1}{v}=0}$

$\sf{\implies v =\dfrac{1}{0}}$

${\underline{\boxed{\pink{\mapsto v=\infty}}}}$

${\bf{\red{\mapsto So\:object\:is\:formed\:at\:infinity}}}$

______________________________________

Since the object is at infinity image will be highly enlarged.So,it's magnification will also be infinity.

$\bf{\green{\underline{\leadsto Magnification}}}$

$\large\purple{\boxed{\boxed{\orange{\bf{\mapsto m= \dfrac{f}{f-u}}}}}}$

$\sf{\implies m=\dfrac{10}{10-10}}$

$\sf{\implies m =\dfrac{10}{0}}$

${\underline{\boxed{\red{\mapsto m =\infty}}}}$

${\bf{\pink{\mapsto So\:magnification\:is\:infinity.}}}$