Question

A child is playing with a bubble wand, which is a large rectangular wire frame that contains a soap film. The child holds the wand vertically, which causes the film to be thinner at the top and thicker at the bottom, forming a wedge shape. Assume a thickness of essentially zero at the top. White light shines on the film with approximately normal incidence. The child views the reflected light from the film and sees the first violet interference band at a distance of 3.00 cm from the top edge of the film. The index of refraction of the soap film is the same as that of water, n-1.33, and the wavelength of violet light is λ-402 nm fim with appro band at a distance of 3.00 and the wavelengf (a) At what distance (in cm) from the top edge of the film does the child see the first red 687 nm) interference band? cm (b) What is the thickness (in nm) of the soap film at the location of the first violet interference band? tiar What is the thickness (in nm) of the soap film at the location of the first red interference band? nm (c) What is the wedge angle of the film (in rad)? rad

Answer 1

One phase reversal occurs by reflection off the front of the soap film. (a) Bright bands are observed when 2nt A 2 Hence, the first bright band (m - 0) corresponds to nt By similar triangles, the distance x from the top where a fringe occurs is proportional to the thickness t of the film: or Thus, we have -60 687 nm 402 nm (3.00 cm) 5.13 cm 402 nm 75.6 nm 4n 4(1.33) 4 4 1.33)

, 75.6 nm x 3.00 cm 2.52x 10-6 rad

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