Question

how can i prove mirror formula

Answer 1

The following sign convention is used for measuring various distances in the Ray diagrams of spherical mirrors:

All distances are measured from the pole of mirror.

Distance measured in the direction of incident Ray are positive and the distance measured in the direction opposite to that of the incident Ray's and negative.
Distance measured above the principal axis are positive and that measured below the principal axis are negative.

angle A1 CB1 = angle ACB (vertically opposite angles)

angle AB1 C = angle ABC (right angles)

when two angles of DA1 CB1 and D ACB are equal then the third angle.
angle B1A1C1 = angle BAC
∆ A1 CB1 and ∆ ACB are similar
AB/A1B1 = BC /C1B1 ------> (1)

similarly ∆ FB1A1 and ∆ FED are similar
ED /A1B1 = EF/ FB1
AB/A1B1 =EF /FB1 -------> (2)
From equation (1) and (2)
BC/B1C =EF /FB1

BC/B1C =PF/FB1
BC= PB1-PC
B1C =PB1 -PC
PC-PB/PB1-Pc = PF/PB1-PF --------->(3)

From equation (3)
-R-(-U) /-V-(-R) =-F /-V-(-F)
-R+U/-V+R=-F /V-F
U-R /R-V = F/V-F
UV-UF -RV=RF -RF-VF
2=2F

UV-UF-2FV =-VF
UV-UF =2FV -FV
UV-UF =VF ------> (4)

Deriving equation (4)
1/F-1/v=1/U
1/F = 1/V+ 1/G--------->(5)

By equation (5) Gives the mirror formula

Hope this helps you friend
Thanks ✌️ ✌️

Answer 2

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