Question

Q.10 Prove that 1/f=1/v+1/u for a concave mirror.​

Answer 1

Prove:

• 1/f = 1/v + 1/u ( for a concave mirror )

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This a lens formula which gives us relation between focal length, distance of object and distance of image from a optical centre.

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Proof:

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Refer the attachment for a ray diagram.

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Here, ( from the attachment )

• O = optical centre
• F = Principal focus
• f = focal length
• u = distance of object
• v = distance of image from a optical centre.

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Let AB be the object which is perpendicular to Principal axis.

Real, inverted and magnified image is formed.

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∆ABO and ∆A' B' O are similar

$\sf \dfrac{A'B'}{AB} = \dfrac{OB'}{OB}$

Now, ∆A' B' F and ∆OCF are similar

$\sf \dfrac{A'B'}{OC} = \dfrac{FB'}{OF}$

OC = AB

$\sf \dfrac{A'B'}{AB} = \dfrac{FB'}{OF}$

Now, from it we get:

For next steps refer the second attachment.

At last...

Hence Proved!!

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