Question

establish mirror formula for a concave mirror​

Answer 1

Answer:

Hello,

mirror formula is always same for all type of mirrors.

that is,

$\frac{1}{f } = \frac{1}{v} + \frac{1}{u}$

Hope it helps...

Answer 2

$\Large\underline\mathfrak{Question}$

Establish mirror formula for a concave mirror.

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→ Check the attachment first provided with answer.

→ We need to Learn about Sign Conventions before deriving mirror formula as it involve "The sign conversations.

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$\Large\bold\star\underline{\underline\textbf{Mirror formula\:}}$

→ See the attachment .

→ Consider an object AB lying beyond the principal focus F of a concave mirror.

→ Let BK and BL be the two incident rays which meet at point B' after reflection from the mirror.

→ A'B' be the image of object AB.

→ Draw KN perpendicular to principal axis.

→ Now ∆ NKF and ∆ A'B'F are similar, therefore

» A'B' / KN = A' F /NF.....................(1)

→ When aperture of mirror is small then point N is very close to P. So, NF ≈ PF (approx) and KN ≈ AB

→ Equation (1) becomes,

A'B / AB = A'F / PF ..........................(2).

→ Also ∆ ABC and ∆ A'B'C are similar, therefore

A'B' / AB = A'C / AC ........................(3).

→ From equations (2) and (3), we have

A'F / PF = A'C / AC

(Or)

PA' - PF / PF = PC - PA' / PA -PC

..................(4)

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→ Using Sign Conventions , We have,

» PA' = - v

» PF = - f

» PC = R = - 2f

» PA = - u

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→ So , Equation (4) becomes

» - v + f / - f = - 2f + v / - u + 2f

» uv - 2vf - uf + 2f² = 2f² - vf

» uv - uf = vf.............(5)

Dividing equation (5) by uvf , we get

1 / f - 1 / v = 1 / u

Or

1 / f = 1 / u + 1 / v

This equation is called mirror formula.

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Hope it helped u.

$\huge\bold{\red{\ddot{\smile}}}$