n
1
n
2
θ
1
θ
2
α
β
γ
Refraction at a curved surface
•
h/p=tan
α
≈
α
=
θ
1

γ
=
θ
1
h/R
•
h/i=tan
β
≈
β
=
γ

θ
2
•
h/R=tan
γ
≈
γ
•
γ
=
θ
2
+b
•
θ
1
=
α
+
γ
•
n
1
θ
1
=n
2
θ
2
•
n
1
h/p+n
2
h/i=n
1
θ
1
n
2
θ
2
+(n
2
n
1
)h/R
•
n
1
/p+n
2
/i=(n
2
n
1
)/R
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A Lens
•
Suppose n
1
=1 (air), and we attach a second piece of
concave transparent mirror to the first.
Call R
1
and R
2
the radii of curvatures.
•
If we keep the pieces of glass thin, use the image of the
first surface for the object for the second, and adopt the
convention that if rays converge towards the object then
we define the distance to be negative, then we get the
lens makers formula:
•
1/o+1/i=(n1)(1/R
1
1/R
2
)=1/f
.
•
Where
1/f=(n1)(1/R
1
1/R
2
).
•
There is much that is useful here, especially if we pay
attention to signs.