Question

Please derive the mirror formula for concave mirror

Answer 1

actually mirror formula is 1/f = 1/u + 1/v . but in caze of concave mirror , u=negative , v= negative , f= negative in all cases except object is b/ w pole and focus. if u substitute these values. in it u will get required formula si, 1/-f =1/- v + 1/-u so, 1/-f = -u-v /uv then, f=uv / u+v.hope you understand please mark brainliest.

Answer 2

$\Large\underline\mathfrak{Question}$

Please derive the mirror formula for concave mirror.

$\rule{200}{4}$

$\bold{\boxed{\large{\boxed{\orange{\small{\boxed{\large{\red{\bold{\:ANSWER}}}}}}}}}}$

$\rule{200}{4}$

→ Check the attachment first provided with answer.

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

$\rule{200}{4}$

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

→ 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)

$\rule{200}{4}$

→ Using Sign Conventions , We have,

» PA' = - v

» PF = - f

» PC = R = - 2f

» PA = - u

$\rule{200}{4}$

→ So , Equation (4) becomes

$\frac{ - v \: + \: f \: }{ - f} = \frac{ - 2f \: + \: v \: }{ - u \: + \: 2f}$

$uv - 2vf - uf + {2f}^{2} = {2f}^{2} - vf$

$uv - uf = vf...........(5)$

Dividing equation (5) by uvf , we get

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

Or

$</p><p> \frac{1}{f } = \frac{1}{u} + \frac{1}{v}$

This equation is called mirror formula.

$\rule{200}{4}$

Hope it helped u.

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