c) The primary mirror of the James Webb Space Telescope consists of 18 hexagonal seg- ments. To measure the step (height offset) between two adjacent segments, a blocker is inserted in the science instrument to only view a small patch of the mirror across two neighboring segments. The light from a star on this patch is then dispersed in wavelength via a grating, with a linear dispersion of 10 μm nm-1 onto a detector, with the wavelength of 1500 nm falling at the centre of the detector. Bright fringes are observed at -2.5 and +2.5 mm from the centre of the detector, with a further 41 bright and 42 dark fringes near equally spaced in between these positions. Calculate the step offset between the two mirror segments.

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c) The primary mirror of the James Webb Space Telescope consists of 18 hexagonal seg-
ments. To measure the step (height offset) between two adjacent segments, a blocker
is inserted in the science instrument to only view a small patch of the mirror across two
neighboring segments. The light from a star on this patch is then dispersed in wavelength
via a grating, with a linear dispersion of 10 μm nm-1 onto a detector, with the wavelength of
1500 nm falling at the centre of the detector.
Bright fringes are observed at -2.5 and +2.5 mm from the centre of the detector, with a
further 41 bright and 42 dark fringes near equally spaced in between these positions.
Calculate the step offset between the two mirror segments.
Transcribed Image Text:c) The primary mirror of the James Webb Space Telescope consists of 18 hexagonal seg- ments. To measure the step (height offset) between two adjacent segments, a blocker is inserted in the science instrument to only view a small patch of the mirror across two neighboring segments. The light from a star on this patch is then dispersed in wavelength via a grating, with a linear dispersion of 10 μm nm-1 onto a detector, with the wavelength of 1500 nm falling at the centre of the detector. Bright fringes are observed at -2.5 and +2.5 mm from the centre of the detector, with a further 41 bright and 42 dark fringes near equally spaced in between these positions. Calculate the step offset between the two mirror segments.
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