How do you derive the lens maker's equation?

Using Snell’s law ( n1 sin θi = n2 sin θr ) at point A gives

1)        sin i1 = n sin r1             

2)        i1 = n r1

3)        i1 = α1 + β1

4)        r1 = β1 - γ

5)        α1 + β1 = n(β1 - γ)

6)        sin i2 = n sin r2

7)        i2 = n r2

8)        i2 = α2 + β2

9)        r2 = β2 + γ

10)      α2 + β2 = n(β2 + γ)

11)      α1 + α2 = (n - 1)(β1 + β2)

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

describing distributions is one of the key skills you’ll need to earn a high score on the ap statistics exam. if you need proof of this, just flip through some past exam questions, which can be found at the collegeboard website. you’ll notice that the first free response question is almost always a question requiring you to look at a graph and describe it.

step-by-step explanation: just trying to get points sorry : (