# The Refracting Surface Formula

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**The Refracting Surface Formula**

The incident ray from point object 0 in 0 that falls on point a of a spherical refracting surface is refracted there according to n, sin 0, = n2 sin °2,

If a is small, 0 , and ~ will also be small and we can replace the sines of theseangles with the angles themselves. Thus, the equation above becomes We again use the fact that an exterior angle of a triangle is equal to the sum of the

two opposite interior angles. Applying this to triangles COa and ICa yields

0, = a + 13 and 13 = O2 + ‘Y. If we use Eqs. 35-19 to eliminate 0, and O2 from Eq. 35-18, we find

n,a + n2’Y = (n2 – 11,) In radian measure the angles a, 13, and ‘Yare (35-19) t

(35-20)

a~-o;c

p

ac 13 =-;

r

(35-21)

oc

‘Y= -; .