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In Figure (a), the waves along rays 1 and 2 are initially in phase, with the same wavelength A in air. Ray 2 goes through a material with length L and index of refraction n. The rays are then reflected by mirrors to a common point P on a screen. Suppose that we can vary n from n = 1.00 to n = 2.83. Suppose also that, from n = 1.0 to n = ng = 1.05, the intensity I of the light at point P varies with n as given in Figure (b). At what values of n greater than 1.04 is intensity I (a) maximum and (b) zero? (c) What multiple of A gives the phase difference between the rays at point P when n = 1.10? Screen Ray 2 Ray 1 ng (a) (b)

In Figure (a), the waves along rays 1 and 2 are initially in phase, with the same wavelength A in air. Ray 2 goes through a material with length L and index of refraction n. The rays are then reflected by mirrors to a common point P on a screen. Suppose that we can vary n from n = 1.00 to n = 2.83. Suppose also that, from n = 1.0 to n = ng = 1.05, the intensity I of the light at point P varies with n as given in Figure (b). At what values of n greater than 1.04 is intensity I (a) maximum and (b) zero? (c) What multiple of A gives the phase difference between the rays at point P when n = 1.10? Screen Ray 2 Ray 1 ng (a) (b)

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### Chapter 35, Problem 086 GO In Figure (a), the waves along rays 1 and 2 are initially in phase, with the same wavelength \( \lambda \) in air. Ray 2 goes through a material with length \( L \) and index of refraction \( n \). The rays are then reflected by mirrors to a common point \( P \) on a screen. Suppose that we can vary \( n \) from \( n=1.00 \) to \( n=2.83 \). Suppose also that, from \( n=1.00 \) to \( n=n_s=1.05 \), the intensity \( I \) of the light at point \( P \) varies with \( n \) as given in Figure (b). At what values of \( n \) greater than 1.04 is intensity \( I \) (a) maximum and (b) zero? (c) What multiple of \( \lambda \) gives the phase difference between the rays at point \( P \) when \( n=1.10 \)? **Diagrams:** - **Figure (a):** A schematic showing ray 1 and ray 2 initially in phase and with the same wavelength \( \lambda \). Ray 2 passes through a material of index of refraction \( n \) with a length \( L \). Both rays are then reflected by mirrors to a point \( P \) on a screen. - **Figure (b):** A graph showing the variation of intensity \( I \) with respect to the refractive index \( n \). The graph indicates that as \( n \) increases from 1 to \( n_s = 1.05 \), the intensity changes, following a specific pattern. **Solutions:** (a) Number \( \underline{\hspace{1cm}} \) * 1 Units \( \underline{\hspace{5cm}} \) (b) Number \( \underline{\hspace{1cm}} \) * 2 Units \( \underline{\hspace{5cm}} \) (c) Number \( \underline{\hspace{1cm}} \) * 3 Units \( \underline{\hspace{5cm}} \) ### Explanation of Figures: **Figure (a):** - Shows two rays initially in phase. - Ray 2 passes through a block with refractive index \( n \) and a length \( L
Transcribed Image Text:### Chapter 35, Problem 086 GO In Figure (a), the waves along rays 1 and 2 are initially in phase, with the same wavelength \( \lambda \) in air. Ray 2 goes through a material with length \( L \) and index of refraction \( n \). The rays are then reflected by mirrors to a common point \( P \) on a screen. Suppose that we can vary \( n \) from \( n=1.00 \) to \( n=2.83 \). Suppose also that, from \( n=1.00 \) to \( n=n_s=1.05 \), the intensity \( I \) of the light at point \( P \) varies with \( n \) as given in Figure (b). At what values of \( n \) greater than 1.04 is intensity \( I \) (a) maximum and (b) zero? (c) What multiple of \( \lambda \) gives the phase difference between the rays at point \( P \) when \( n=1.10 \)? **Diagrams:** - **Figure (a):** A schematic showing ray 1 and ray 2 initially in phase and with the same wavelength \( \lambda \). Ray 2 passes through a material of index of refraction \( n \) with a length \( L \). Both rays are then reflected by mirrors to a point \( P \) on a screen. - **Figure (b):** A graph showing the variation of intensity \( I \) with respect to the refractive index \( n \). The graph indicates that as \( n \) increases from 1 to \( n_s = 1.05 \), the intensity changes, following a specific pattern. **Solutions:** (a) Number \( \underline{\hspace{1cm}} \) * 1 Units \( \underline{\hspace{5cm}} \) (b) Number \( \underline{\hspace{1cm}} \) * 2 Units \( \underline{\hspace{5cm}} \) (c) Number \( \underline{\hspace{1cm}} \) * 3 Units \( \underline{\hspace{5cm}} \) ### Explanation of Figures: **Figure (a):** - Shows two rays initially in phase. - Ray 2 passes through a block with refractive index \( n \) and a length \( L
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