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Figures (3)

F. 1
F. 1

Graphic calculation of a biconvex lens; X optical axis, Z graph axis, Q graph centre, O1O2 centres of curvature of surfaces 1 and 2, r1r2 radii to points of refraction, p1p2 intercepts of incident and refracted ray on reference planes, p′1 p′2 intercepts of segment of ray within the glass, 1 and 2 lens surfaces and the corresponding graphs.

F. 2
F. 2

Lenses of a Huygenian eyepiece so drawn that the two curved surfaces have a common centre, p2 intercept of the ray in the eye lens, p′1 intercept of the ray passing from eye lens to field lens, p′4 intercept of the ray in the field lens, and p4 intercept of the ray below the field lens.

F. 3
F. 3

Ray intercepts on a plane tangent to the lens vertex α, α′, θ and θ′ the angles made by the incident and refracted rays with the radius at the point of refraction and with the optical axis, p p′ the intercepts on the vertex plane of the incident and refracted rays, h, h′ and h″ the difference between the height of the incident point from the optical axis and these intercepts and that of the radius.

Equations (22)

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sin α = o sin θ r
sin α = sin α n
θ = θ + α α
o = r sin α sin θ
o = o + d
sin α = o sin θ r
sin α = n sin α
θ = θ + α α
o = r sin α sin θ
1 o m = 1 o 1 + k = 1 k = m sin φ k r k ( cot α k cot α k )
sin α = p cos θ r
p = r sin α cos θ
p = p + dt
o = p / tang θ
u = r o
h + h + p = r tan ( α θ )
h = h tan ( α θ ) tan θ
h = r tan ( α θ ) p 1 tan ( α θ ) tan θ
h = h tan θ tan θ
p = p + h h
p = p tan θ tan θ tan θ tan ( α θ ) { r tan ( α θ ) p }
p = 17.39132 .025809 .0157872 .0157872 .0004348 ( 40000 × .0004348 17.39132 ) = 17.39132 .0100438 .005743 .00065 = 17.39132 .00114 = 17.39018