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Though I know that wave transverse while striking a denser medium shows a 180 degree phase shift but why this shift doesn't occur while a wave is reflected from a lighter medium.

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You can derive this from the junction condition of the fields at the border of the media, as known as Maxwell equations for plane waves at the border of two media.

You can find a complete derivation in paragraph 7.3 of J.D. Jackson, Classical Electrodynamics. The end of the paragraph is exactly checking that what you asked is true.

Google suggested this link if you need the book.

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  • $\begingroup$ Would be so candid of you if you added that paragraph here. $\endgroup$ Commented Jun 25, 2018 at 11:31

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