Question

In an optics laboratory, a researcher has performed Young's double slit experiment with two coherent beams with each wavelength of 2.0 mm. They both travel 4 cm to a detector, but one passes through air while the other through an unknown liquid of refractive index of 2.0

a) Do they cause constructive or destructive interference ?

b) Suppose if you replace the given liquid with other liquid of refractive index 2.5, will you get the same answer? Justify your answer

Answer 1

Distance to the detector: 40 mm, wavelength is 2 mm.

a) The interference is constructive because the wavelength in the liquid is 2 times shorter (because the refractive index is 2). Calculate how many complete waves fill the 40 mm to the detector and the path difference:

$$\Delta x=40/(2/2)-40/2=10·2=10\lambda.$$

b) Calculate the path difference in this case:

$$\Delta x=40/(2/2.5)-40/2=15·2=15\lambda.$$

The interference is constructive.