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answerhappygod
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4. A linearly polarised beam of light, of wavelength in vacuum of 600 nm and optical power 1 mW, is incident on an instrument made of: a linear polariser (P1) with its direction of transmission at 45 degrees with respect to the x-direction, a quarter-wave plate (WP) of thickness L and a second linear polariser (P2) oriented in the same way as P1. The Jones matrix associated with the 2 polarisers is, Jis = 12 (11) J45 WP is rotated in such a way that its eigenaxes are parallel to the x and y-direction. The birefringent material used for WP has refractive indices associated with its eigenaxes, 2.201 and 2.202. The incident beam of light is linearly polarised at 60 degrees with respect to the x-direction. E 60⁰ P₁ WP (a) Derive an expression for the Jones vector describing the state of polarisation of the incident beam. (b) After WP, light is circularly polarised. Use Jones calculus to find out the thickness of WP. (c) Determine the state of polarisation after each component. Comment on how the optical power is changed by P₁, WP and P₂. (d) P1 is replaced by a linear polariser with its transmission along the x-direction whereas WP is replaced by an optically active medium characterised by a Jones matrix, cos p sin p JOA = sin p cos p The rotatory power p, is the angle by which the active medium changes the polarisation direction of the incident, linearly polarised beam of light. Use Jones calculus to find p for which there is no light after P2. (e) Demonstrate that any linearly polarised state can be decomposed into a sum of right and left circularly polarised states of equal amplitudes. Write the expressions of the Jones vectors for the two circularly polarised states, in which a linearly polarised state in the x-direction can be decomposed. [5 marks] [5 marks] [5 marks] [5 marks] [5 marks]
4. A linearly polarised beam of light, of wavelength in vacuum of 600 nm and optical power 1 mW, is incident on an instrument made of: a linear polariser (P1) with its direction of transmission at 45 degrees with respect to the x-direction, a quarter-wave plate (WP) of thickness L and a second linear polariser (P2) oriented in the same way as P1. The Jones matrix associated with the 2 polarisers is, Jis = 12 (11) J45 WP is rotated in such a way that its eigenaxes are parallel to the x and y-direction. The birefringent material used for WP has refractive indices associated with its eigenaxes, 2.201 and 2.202. The incident beam of light is linearly polarised at 60 degrees with respect to the x-direction. E 60⁰ P₁ WP (a) Derive an expression for the Jones vector describing the state of polarisation of the incident beam. (b) After WP, light is circularly polarised. Use Jones calculus to find out the thickness of WP. (c) Determine the state of polarisation after each component. Comment on how the optical power is changed by P₁, WP and P₂. (d) P1 is replaced by a linear polariser with its transmission along the x-direction whereas WP is replaced by an optically active medium characterised by a Jones matrix, cos p sin p JOA = sin p cos p The rotatory power p, is the angle by which the active medium changes the polarisation direction of the incident, linearly polarised beam of light. Use Jones calculus to find p for which there is no light after P2. (e) Demonstrate that any linearly polarised state can be decomposed into a sum of right and left circularly polarised states of equal amplitudes. Write the expressions of the Jones vectors for the two circularly polarised states, in which a linearly polarised state in the x-direction can be decomposed. [5 marks] [5 marks] [5 marks] [5 marks] [5 marks]