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The sine and tangent small-angle approximations are used in relation to the double-slit experiment or a diffraction grating to develop simplified equations like the following, where y is the distance of a fringe from the center of maximum light intensity, m is the order of the fringe, D is the distance between the slits and projection screen ...
Fig. 1 Isosceles skinny triangle. In trigonometry, a skinny triangle is a triangle whose height is much greater than its base. The solution of such triangles can be greatly simplified by using the approximation that the sine of a small angle is equal to that angle in radians.
However, small-disturbance subsonic compressible flow can be modeled if the general 3D Prandtl-Glauert transformation is incorporated into the method. The lifting surfaces are thin. The influence of thickness on aerodynamic forces are neglected. The angle of attack and the angle of sideslip are both small, small angle approximation.
where G, R g, and B are constants related to the scattering contrast, structural volume, surface area, and radius of gyration. q is the magnitude of the scattering vector which is related to the Bragg spacing, d, q = 2π/d = 4π/λ sin(θ/2). λ is the wavelength and θ is the scattering angle (2θ in diffraction).
Geometrical optics is often simplified by making the paraxial approximation, or "small angle approximation". The mathematical behavior then becomes linear , allowing optical components and systems to be described by simple matrices.
In geometric optics, the paraxial approximation is a small-angle approximation used in Gaussian optics and ray tracing of light through an optical system (such as a lens). [1] [2] A paraxial ray is a ray that makes a small angle (θ) to the optical axis of the system, and lies close to the axis throughout the system. [1]
Suppose the freestream flow attacks the airfoil at position y at angle α(y) (relative to the liftless angle for the airfoil at position y — thus a uniform flow across a wing may still have varying α(y)). By the small-angle approximation, the effective angle of attack at y of the combined freestream and vortex system is α(y)+ w(y) ⁄ V ...
When α is very small (α < π / 6 ) the following small-angle approximations can be made: thus . We can see that the smaller α is, the farther apart the pale lines; when both patterns are parallel ( α = 0 ), the spacing between the pale lines is infinite (there is no pale line).