Physic Labs

Problem 3

Monochromatic light of wavelength λ\lambda passes through two narrow slits separated by dd onto a screen distance LL away, with L≫dL\gg d. Find the fringe spacing ii and position of bright fringe order mm from the central maximum, using the small-angle approximation. Assume the string, pulley, electrical source, or optical apparatus is ideal as stated, and neglect any effect not specified. State a clear sign convention, identify the physical Keep one model and sign convention throughout. Reuse each intermediate result with the same convention, then check that the answer has the required physical dimensions. (a) Set up the physical relation. (b) Find an intermediate quantity. (c) Obtain the answer and check its conditions and units.
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ym≃Ltan⁡θ≃Lsin⁡θy_m\simeq L\tan\theta\simeq L\sin\theta
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For a screen far from the slits and small angles, the transverse position satisfies y≃Lsin⁡θy\simeq L\sin\theta. This is consistent with the stated model and the chosen sign convention.