Question

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Answer 1

Answer:

Mirror formula is the relationship between  image distance (v), focal length (f) and object distance (u) .

Explanation:

Mirror formula:

1/v+1/u=1/f

Where image distance (v), focal length (f) and object distance (u).

Proof of the mirror formula (considering concave mirror):

In ΔABC and ΔA′B′C′

ΔABC ∼ ΔA′B′C [AA similarity]

AB / A′B′=AC / A′C′ ------------------- (1)

Similarly, In ΔFPEand ΔA′B′F′

EP / A′B′=PF / A′F

AB / A′B′=PF / A′F [ AB=EP] ------------- (2)

From (1) and (2)

AC / A′C=PF / A′F

=>A′C / AC=A′F / PF

=>(CP−A′P) / (AP−CP)=(A′P–PF) /PF

Now, PF =−f; CP =2PF=−2f ; AP=−u ; and A′P= −v

Put these value in above relation:

⟹[(−2f)–(−v)] / (−u)−(−2f) = [(−v)–(−f)] / (−f)

⟹uv=fv+uf

⟹1 / f=1 / u + 1 / v

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