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6. A Michelson interferometer consists of a beamsplitter that divides a laser beam of wavelength \( \lambda \) and intensity \( I_{0} \) into two equal amplitude 'arms' with lengths \( l \) and \( l+d \). The beam in each arm may be approximated as a plane wave. A precision motor enables \( d \) to be smoothly varied. Two perfect mirrors retroreflect the light such that the two paths interfere at the beamsplitter. (a) Calculate the Rayleigh length of the laser beam if the beam waist is \( 0.01 \mathrm{~m} \) and the wavelength is \( 1.06 \mu \mathrm{m} \), and discuss why the plane wave approximation is reasonable if the maximum arm length \( l+d<10 \mathrm{~m} \). [4 marks]

          6. A Michelson interferometer consists of a beamsplitter that divides a laser beam of wavelength \( \lambda \) and intensity \( I_{0} \) into two equal amplitude 'arms' with lengths \( l \) and \( l+d \). The beam in each arm may be approximated as a plane wave. A precision motor enables \( d \) to be smoothly varied. Two perfect mirrors retroreflect the light such that the two paths interfere at the beamsplitter.
(a) Calculate the Rayleigh length of the laser beam if the beam waist is \( 0.01 \mathrm{~m} \) and the wavelength is \( 1.06 \mu \mathrm{m} \), and discuss why the plane wave approximation is reasonable if the maximum arm length \( l+d<10 \mathrm{~m} \). [4 marks]

6. A Michelson interferometer consists of a beamsplitter that divides a laser beam of wavelength λ and intensity I0 into two equal amplitude 'arms' with lengths l and l+d. The beam in each arm may be approximated as a plane wave. A precision motor enables d to be smoothly varied. Two perfect mirrors retroreflect the light such that the two paths interfere at the beamsplitter.
(a) Calculate the Rayleigh length of the laser beam if the beam waist is 0.01 m and the wavelength is 1.06 μm, and discuss why the plane wave approximation is reasonable if the maximum arm length l+d<10 m. [4 marks]

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