Physics, asked by ankita10899, 7 hours ago

prove that for any spherical mirror 1/f=1/v+1/u where the symbols have their usual meaning​

Answers

Answered by shamayelrahman0786
2

Answer:

Refer to the mirror formula, 1v + 1u = 1f , where the symbols have their usual meanings. Which of the following graphs correctly depicts this variation

Explanation:

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Answered by gayatrikumari99sl
0

Answer:

We proved that \frac{1}{f} = \frac{1}{v} +\frac{1}{u} for  any spherical mirror .

Explanation:

First we draw a diagram of spherical mirror and

Let an object AB is place in front of the mirror .

Let u be the distance between the object and the mirror ,

let v be the distance between the image and mirror and

let f be the focal length .

 Now from the diagram we have B'P = -v , PF = -f and BP = -u

Now ,ΔB'A'F and ΔFPM are similar

∠A'B'F = 90 =∠MPF = 90  ∠A'FB'= ∠PFM  so the other angles is also equal .

\frac{B'A'}{PM} = \frac{B'F}{PF}

\frac{B'A'}{BA} =\frac{B'F}{PF}  ......(i)       [PM = BA ]

Similarly , ΔA'B'P and ΔABP are similar ,

\frac{B'A'}{BA}  = \frac{B'P}{BP} ..........(ii)

From (i) and (ii) we get ,

\frac{B'F}{PF}  = \frac{B'P}{BP}

\frac{B'P - PF }{PF}  = \frac{B'P}{BP}   .........(iii)      [B'F = B'P - PF ]

Now put the value of B'P , PF and BP in (iii) we get

\frac{-v +f  }{-f}  = \frac{-v}{-u}

\frac{v  -f  }{f}  = \frac{v}{u}  

⇒ uv - uf = vf       [By cross multiplication]

Now divide both the side by uvf   we get ,

\frac{uv}{uvf} -\frac{fu}{uvf} =\frac{vf}{uvf}

\frac{1}{f} -\frac{1}{v} =\frac{1}{u}\frac{1}{f} = \frac{1}{v} +\frac{1}{u}  proved .

Hence , here we proved that \frac{1}{f} = \frac{1}{v} +\frac{1}{u}.

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