1.5.5 Small angle approximations (A-level only)

An optical sensor measures the flux $F\,$ of light entering an aperture at a small angle $\phi\,$ radians. The flux is modelled by the expression:

\frac{1 - \cos(14\phi)}{\phi \sin(7\phi)}

Using small angle approximations, show that for small, non-zero values of $ϕ\phi$ ,

\approx A

where $A\,$ is a constant to be determined.

[4]

An optical sensor measures the flux $F\,$ of light entering an aperture at a small angle $\phi\,$ radians. The flux is modelled by the expression:

\frac{1 - \cos(14\phi)}{\phi \sin(7\phi)}

Using small angle approximations, show that for small, non-zero values of $ϕ\phi$ ,

\approx A

where $A\,$ is a constant to be determined.

[4]

1.5.5 Small angle approximations (A-level only) Questions