Example 2.1 For a sphere of radius r, find the solid angle A (in square radians or steradians) of a spherical cap on the

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Example 2 1 For A Sphere Of Radius R Find The Solid Angle A In Square Radians Or Steradians Of A Spherical Cap On The 1 (64.04 KiB) Viewed 40 times

Attach is a question and its solution. Please, for thesolution, explain clearly the solution for part (b), where did theyget the value pi/3. Upvote for a clear explanation.Thanks.
Example 2.1 For a sphere of radius r, find the solid angle A (in square radians or steradians) of a spherical cap on the surface of the sphere over the north-pole region defined by spherical angles of 0 ≤ 0 ≤ 30°, 0≤ ≤ 180°. Refer to Figures 2.1 and 2.10. Do this a. exactly. b. using A₁ A₂, where AO₁ and AO2 are two perpendicular angular separations of the spherical cap passing through the north pole. Compare the two. .
Solution: a. Using (2-2), we can write that 360° 30° 2л pπ/6 - 136 1²h dra = 1²th for si dQ= SZA = Cπ/6 = ²* ¢¢ ƒ™¹²; sin 0 de do = = = 2л[− cos 0]|T/6 = 2π[−0.867 +1] = 2 (0.133) = 0.83566 Ae₁=A₂ b. Ωχ ~ ΔΕΗ· ΔΘ2 (0)² = 7 (7) = 7² (ΔΘ)2 3 It is apparent that the approximate beam solid angle is about 31.23% in error. sinᎾ dᎾ = 1.09662