Question

prove mirrors fromula

Answer 1

Answer:

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

1/v + 1/u = 1/f

In Triangle ABC and Triangle A’B’C

<A = <A’ = 900

<C =<C ( vert. opp. <s]

Triangle ABC ~Triangle A’B’C [AA similarity] => AB /A’B’ = AC/A’C ----(I)

Similarly,

In Triangle ABC and A’B’C

<A = <A’ = 900

<C =<C ( vert. opp. <s]

Also, in Triangle ABC ~Triangle A’B’C [AA similarity]

AB /A’B’ = AC/A’C ----(1)

Similarly, In DFPE ~ A’B’F

EP /A’B’ = PF/A’F

AB /A’B’ = PF/A’F [ AB=EP] ----(II)

From(i) &(ii)

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

HOPE IT HELPS.................................

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Answer 2

Answer:

this is proved by triangle similarly....

hope this will help you