how to derive the mirror formula explain with diagram
Answers
HEY MATE .....
Mirror formula is the relationship between object distance (u), image distance (v) and focal length (f).
A ray of light starting from A and incident on the mirror along AD parallel to the principal axis of the mirror and gets reflected from the mirror and passes through F.
Another ray of light incident along AP is reflected along PA’ such that angle APB=i= angle BPA’= r.
The two reflected ray meet at A’ which is a real image.
Therefore A’B’ is real, inverted image of AB formed by reflection from the mirror.
In Triangles BAC and A’B’C’
AB/A’B’ = CB/CB’ ……………. (i)
Now Triangle ABP and A’B’P’ are similar,
AB/A’B’ = PB/PB’ …………………. (ii)
From (i) & (ii) …
CB/CB’= PB/PB’ ……………….. (iii)
Measuring all distances from P,
We have CB= PB-PC CB’= PC-PB’
Therefore from (iii),
(PB-PC)/(PC-PB’) = PB/PB’ …………… (iv)
Using new cartesian sign convections,
PB= -u (distance of object) PC= -R PB’ = -v (distance of image) We get from (iv), (-u+R)/(-R+v) = -u/-v
Or,
+uR – uv = uv – vR Or,
uR + vR = 2uv
Dividing both sides by uvR,
We get, 1/v + 1/u = 2/R As
R=2f
Therefore, 1/v + 1/u = 2/R = 2/2f = 1/f This is the required formula.
HOPE IT WILL HELP YOU......
Answer:
Here is your answer
Explanation:
You can see that the triangles shaded are congruent
Thank you
