Assume the indices of refraction for air, water, and glass are 1.00, 1.33, and 1.50, respectively. When illuminated from above, a ray reflected from the air-water interface undergoes a phase shift of φ 1 = π, and a ray reflected at the water-glass interface also undergoes a phase shift of π. Thus, the two rays are unshifted in phase relative to each other due to reflection. For constructive interference, the path difference 2t must equal an integer number (m) of wavelengths in water. a. Derive the equation in terms of λ based on the situation above. b. If this m-value is an integer the wavelength undergoes constructive interference upon reflection in terms of λ, compute for the wavelengths for the following thickness: t= 2 x 10 5 m at m 700 nm and m 400 nm

Assume the indices of refraction for air, water, and glass are 1.00, 1.33, and 1.50, respectively. When illuminated from above, a ray reflected from the air-water interface undergoes a phase shift of φ 1 = π, and a ray reflected at the water-glass interface also undergoes a phase shift of π. Thus, the two rays are unshifted in phase relative to each other due to reflection. For constructive interference, the path difference 2t must equal an integer number (m) of wavelengths in water. a. Derive the equation in terms of λ based on the situation above. b. If this m-value is an integer the wavelength undergoes constructive interference upon reflection in terms of λ, compute for the wavelengths for the following thickness: t= 2 x 10 5 m at m 700 nm and m 400 nm