Part 1: In a double-slit experiment, light from two monochromatic light sources

Question

Part 1: In a double-slit experiment, light from two monochromatic light sources passes through the same double slit. The light from the first light source has a wavelength of 552 nm. Two different interference patterns are observed. If the 9th order bright fringe from the first light source coincides with the 12th order bright fringe from the second light source, what is the wavelength of the light coming from the second monochromatic light source?
(in nm)

Part 2 : Polarizers 1 and 3 have their axes of polarization indicated by the black solid lines, perpendicular to each other. Polarizer 2 has an axis of polarization that has an angle of 37.5 deg with respect to the polarization axis of polarizer 1. What percentage of the initial (unpolarized) light intensity passes through?

Explanation / Answer

apply Y = mLR/d

Y1 = 9 * 552nm * R/d

also Y2 = 12* L2 * R/d

as Y1 = Y2 given

9 *552 nm = 12 * L2

L2 = 414 nm

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apply malus law I = I0 cos ^2 (theta)

after passing through first polarizer, Intneisty reduces by 50%

so I1 = I0/2

so I2 = I1 *cos ^2(90-37.5)

I2/I1    = 0.3705

I2/Io = 0.3705/2

I2/i0 = 18.5 %

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