Question

If you are given a concave mirror of radius of curvature of 8cm. How can you find its focal length. Also find the distance of image if the object is placed at a distance of 10cm from the mirror.

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Answer 1

Answer:

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Answer 2

Correct Question :

If you are given a concave mirror of radius of curvature of-8cm. How can you find its focal length. Also find the distance of image if the object is placed at a distance of -10cm from mirror.

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Step-by-step explanation:-

Given :

• Radius of curvature is -8cm

• Type of mirror is concave mirror

• Object distance is -10cm

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To find :

• Focal length

• Image distance

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Formula to be applied :

• Mirror Formula

$\boxed{\sf\dfrac{1}{F}=\dfrac{1}{V}+\dfrac{1}{U}}$

• Radius of curvature=2×Focal length

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Solution :

~Focal length

The radius of curvature is double of the focal length.

So,

$\longrightarrow$Radius of curvature=2(focal length)

$\longrightarrow$-8cm=2(Focal length)

$\longrightarrow$-8cm/2=focal length

$\longrightarrow$-4cm=focal length

So the required focal length of mirror is -4cm..

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~Image distance

To find image distance we have Formula:

$\sf\dfrac{1}{F}=\dfrac{1}{V}+\dfrac{1}{U}$

Here, F means focal length, V means image distance and U means object distance.

By substituting values::

$\longrightarrow\sf\dfrac{1}{-4cm}=\dfrac{1}{V}+\dfrac{1}{-10cm}$

$\longrightarrow\sf\dfrac{1}{-4cm}+\dfrac{1}{10cm}=\dfrac{1}{V}$

$\longrightarrow\sf\dfrac{-5+2}{20cm}=\dfrac{1}{V}$

$\longrightarrow\sf\dfrac{-3}{20cm}=\dfrac{1}{V}$

By cross multiplication, we get::

$\longrightarrow\sf\dfrac{20cm}{-3}=V$

$\longrightarrow\sf -3.33cm=V$

So the image distance is -3.33cm where -ve sign donates that the image is inverted.

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Points to remember :

• Focal length of concave mirror is Always -ve.

• Radius of curvature of concave mirror is always -ve.

• Object distance of concave mirror is always-ve.

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