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4. An air wedge is formed between two flat pieces of glass (each \( 10 \mathrm{~cm} \) long and \( 1 \mathrm{~cm} \) thick) by placing a piece of tissue paper between them as shown below. It is illuminated by a sodium lamp (whose emission is dominated by light with wavelength \( \sim 0.589 \mu \mathrm{m} \) and has a coherence time of \( 2 \times 10^{-12} \) sec.) a) Consider interference between the ray reflected from the glass-air boundary at the top of the air wedge with the ray from the air-glass boundary at the bottom of the air wedge. State the conditions relating the thickness of the film and the wavelength for (i) constructive interference, and (ii) destructive interference. [The wedge angle is very small and so it is reasonable to assume that the wavefronts reflected from the upper and lower surfaces of the air wedge are parallel.] b) If 87 straight parallel fringes are visible over the \( 4 \mathrm{~cm} \) region illustrated in the image above, deduce the thickness of the tissue paper. c) Explain why rays reflected from the upper surface of the upper glass plate and from the lower surface of the lower plate do not contribute to the observed interference pattern.

          4. An air wedge is formed between two flat pieces of glass (each \( 10 \mathrm{~cm} \) long and \( 1 \mathrm{~cm} \) thick) by placing a piece of tissue paper between them as shown below. It is illuminated by a sodium lamp (whose emission is dominated by light with wavelength \( \sim 0.589 \mu \mathrm{m} \) and has a coherence time of \( 2 \times 10^{-12} \) sec.)
a) Consider interference between the ray reflected from the glass-air boundary at the top of the air wedge with the ray from the air-glass boundary at the bottom of the air wedge. State the conditions relating the thickness of the film and the wavelength for (i) constructive interference, and (ii) destructive interference.
[The wedge angle is very small and so it is reasonable to assume that the wavefronts reflected from the upper and lower surfaces of the air wedge are parallel.]
b) If 87 straight parallel fringes are visible over the \( 4 \mathrm{~cm} \) region illustrated in the image above, deduce the thickness of the tissue paper.
c) Explain why rays reflected from the upper surface of the upper glass plate and from the lower surface of the lower plate do not contribute to the observed interference pattern.

4. An air wedge is formed between two flat pieces of glass (each 10 cm long and 1 cm thick) by placing a piece of tissue paper between them as shown below. It is illuminated by a sodium lamp (whose emission is dominated by light with wavelength ∼ 0.589 μm and has a coherence time of 2 × 10^-12 sec.)
a) Consider interference between the ray reflected from the glass-air boundary at the top of the air wedge with the ray from the air-glass boundary at the bottom of the air wedge. State the conditions relating the thickness of the film and the wavelength for (i) constructive interference, and (ii) destructive interference.
[The wedge angle is very small and so it is reasonable to assume that the wavefronts reflected from the upper and lower surfaces of the air wedge are parallel.]
b) If 87 straight parallel fringes are visible over the 4 cm region illustrated in the image above, deduce the thickness of the tissue paper.
c) Explain why rays reflected from the upper surface of the upper glass plate and from the lower surface of the lower plate do not contribute to the observed interference pattern.

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