Question

A 5.5 CM needle is placed at 11 CM away from a convex mirror of focal length 13cm. Give the location of the image and the magnification.
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Answer 1

Answer :

• Image distance, v = 71.5 cm
• Magnification, m = -5.5 cm

Explanation :

Given :

• Height of the object, h = 5.5 cm
• Object distance, u = 11 cm
• Focal length, f = 13 cm

To find :

• Image distance, v = ?
• Magnification, m = ?

Knowledge required :

• Mirror formula :

⠀⠀⠀⠀⠀⠀⠀⠀⠀1/f = 1/v + 1/u

[Where, f = Focal length; v = Image distance; u = Object distance]

• Magnification :

⠀⠀⠀⠀⠀⠀⠀⠀⠀m = - v/u

[Where, m = magnification; v = Image distance; u = Object distance]

Solution :

Image distance :

By using the mirror formula and substituting the values in it, we get :

⠀⠀=> 1/f = 1/v + 1/u

⠀⠀=> 1/(-13) = 1/v + 1/(-11)

⠀⠀=> 1/(-13) = 1/v - 1/11

⠀⠀=> 1/(-13) + 1/11 = 1/v

⠀⠀=> (-11 + 13)/143 = 1/v

⠀⠀=> 2/143 = 1/v

⠀⠀=> v = 143/2

⠀⠀=> v = 71.5 cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ v = 71.5 cm

Magnification :

By using the formula for magnification and substituting the values in it, we get :

⠀⠀=> m = - v/u

⠀⠀=> m = - (-71.5)/(-13)

⠀⠀=> m = - 71.5/13

⠀⠀=> m = - 5.5

⠀⠀⠀⠀⠀⠀⠀⠀⠀∴ m = -5.5

Therefore,

• Image distance, v = 71.5 cm
• Magnification, m = - 5.5

Answer 2

Answer:

Given :-

• A 5.5 cm needle is placed at 11 cm away from a convex mirror of focal length 13 cm.

To Find :-

• Image distance.
• Magnification

Formula Used :-

❶ To find image distance we have to use the mirror formula,

$\tt\mapsto\boxed{\bold{\large{\dfrac{1}{v} + \dfrac{1}{u} = \dfrac{1}{f}}}}$

❷ To find magnification we have to use the magnification formula,

$\tt\mapsto\boxed{\bold{\large{m\: =\: -\: \dfrac{(- v)}{u}}}}$

Solution :-

Given :

• Height of the needle (h) = 5.5 cm
• Object distance (u) = - 11 cm
• Focal length of the convex mirror (f) = - 13 cm

❶ First we have to find the image distance by using mirror formula,

⇒ $\dfrac{1}{v}$ + $\dfrac{1}{(- 11)}$ = $\dfrac{1}{(- 13)}$

⇒ $\dfrac{1}{v}$ = $\dfrac{1}{(- 13)}$ - $\dfrac{1}{11}$

⇒ $\dfrac{1}{v}$ = $\dfrac{(- 11) + 13}{143}$

⇒ $\dfrac{1}{v}$ = $\dfrac{- 11 + 13}{143}$

⇒ $\dfrac{1}{v}$ = $\dfrac{2}{143}$

⇒ $\dfrac{143}{2}$ = v

⇒ 71.5 = v

➠ $\small\bf{\underbrace{\red{v\: =\: 71.5\: cm}}}$

$\therefore$ The image of the needle is $\large{\red{\bold{\underline{71.5\: cm}}}}$ .

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❷ Now we have to find the magnification by using magnification formula,

⇒ m = - $\dfrac{(- 71.5)}{(- 13)}$

⇒ m = - $\dfrac{71.5}{13}$

➠ $\small\bf{\underbrace{\green{m\: =\: -\: 5.5\: cm}}}$

$\therefore$ The magnification of the needle is $\large{\green{\bold{\underline{-\: 5.5\: cm}}}}$ .

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