Establish Relation between U get and u p
Answers
Answer:
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Explanation:
reflected ray for P.
∵ Angle of incidence = Angle of reflection
∴∠APB=∠A
′
PB
Draw a perpendicular from O on the principle axis.
Let it be OQ
ΔA
′
B
′
F and ΔOQF are similar
∴
OQ
A
′
B
′
=
QF
FB
′
∵OQ=AB
∴
AB
A
′
B
′
=
QF
FB
′
.......(i)
ΔA
′
B
′
P and ΔABP is similar
∴
AB
A
′
B
′
=
PB
PB
′
......(ii)
From equation (i) and (ii)
QF
FB
′
=
PB
PB
′
......(iii)
If the aperture of the mirror is small, then the points Q and P will be very near to each other and so, can be replaced by P, QF=PF (Approx)
So equation (iii) become
PF
FB
′
=
PB
PB
′
PF
PB
′
−PF
=
PB
PB
′
......(iv)
By cartesian sign convention
Object distance PB=−u, Image distance PB
′
=−v, Focal length PF=−f
Hence equation (iv) becomes
−f
−v−(−f)
=
−u
−v
Or
−f
−v+f
=
u
v
Or −vf=−uf+uf
Or uv=−uf+uf
Dividing by uvf on both sides, we get
uvf
uv
=
uvf
vf
−
uvf
uf
Or
f
1
=
u
1
+
v
1
Hence, this equation is the relation between u, v, f.
solution