An eccentric physicist inexplicably makes his home in the bilge of a vodka deliv

Question

An eccentric physicist inexplicably makes his home in the bilge of a vodka delivery ship crossing the Atlantic ocean north of the arctic circle. As the physicist forgot to note down the wavelength of a new light source before throwing the packaging overboard he performs a single slit diffraction experiment using a slit of width 110.0 pm. The diffraction pattern is displayed on a screen 3.000 m from the slit and the 1st minima in the diffraction pattern are 1.420 cm either side of the central maximum. (n_air = 1.008.) Disaster strikes at midnight in the form of an iceberg pushed into the path of the ship by a team of vengeful teetotaler polar bears. As the ship sinks and the lab becomes inundated the single slit diffraction experiment becomes submerged in the briny water. The very cold but excited physicist notices that the spacing between the 1st minima and the central maxima of the diffraction pattern changes to 1.066 cm. With the air in his lungs rapidly running out and th

Explanation / Answer

Here,   d * sin(theta) = n * lambda

=>     d * (y/D) = n * lambda

For light source in air

=> (110 * 10-6) * (0.01420/3) = 1 * lambda

=>    lambda = 520.6667 nm           ---------------------->     wavelength of light source in air

For light source in salty water

=> (110 * 10-6) * (0.01066/3) = 1 * lambda

=>    lambda = 390.8666 nm           ---------------------->     wavelength of light source in salty water

=> refractive index of salty water = (520.6667)/(390.8666)

                                                      = 1.3321

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