Question

an object is placed in front of concave mirror radius of curvature is 30 cm at distance of 10 cm. find the position and magnification of image



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Answer 1

Answer :-

→ Position of the image is 30 cm behind the mirror.

→ Magnification is +3 .

Explanation :-

We have :-

• Radius of curvature = 30 cm

• Position of the object = 10 cm

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Firstly, let's calculate focal length of the mirror :-

⇒ f = R/2

⇒ f = 30/2

⇒ f = 15 cm

Since, the mirror is concave :-

• f = -15 cm

• u = - 10 cm

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According to mirror formula :-

1/v + 1/u = 1/f

⇒ 1/v = 1/f - 1/u

⇒ 1/v = 1/(-15) - 1/(-10)

⇒ 1/v = -1/15 - (-1)/10

⇒ 1/v = (-2 + 3)/30

⇒ 1/v = 1/30

⇒ v = 30 cm

Now, putting values in the formula of magnification of spherical mirror :-

m = -(v/u)

⇒ m = -(30/-10)

⇒ m = -(-3)

⇒ m = +3

Answer 2

Given :-

An object is placed in front of concave mirror radius of curvature is 30 cm at distance of 10 cm

To Find :-

Position

Magnification

Solution :-

We know that

Focal length = Radius of curvature/2

⇒ Focal Length = 30/2

⇒ Focal Length = 15 cm

Now

By using lens formula

${\boxed{\red{\underline{\frak{\dfrac{1}{u}+\dfrac{1}{v} = \dfrac{1}{f}}}}}}$

We have

$\begin{cases} \bf Image\;Distance = v\\ \bf Object\;Distance=10\\ \bf Focal \;length = 15\end{cases}$

1/-10 + 1/v = 1/-15

-1/10 + 1/v = -1/15

1/v = -1/15 - 1/10

1/v = -2 + 3/30

1/v = 1/30

On reciprocal

v = 30 cm

We know that

${\boxed{\red{\underline{\frak{M = \dfrac{-v}{u}}}}}}$

M = -(30)/-10

M = 30/10

M = 3/1

M = 3