GATE 2023 ME – Question 56

Metrology and Inspection · Interferometry, form and finish measurement · 2 marks · Numerical answer

An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavelength 0.5 µm, 12 fringes were observed over a length of 15 mm of gauge B. If the gauges are placed 45 mm apart, the height difference of the gauges is ______________ µm.
(Answer in integer)

an optical flat tilted and resting on the top of gauge A and over gauge B, with the distance 45 mm between the gauges and the length of gauge B of 15 mm.

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Correct answer: 9

Explanation

Each fringe corresponds to a change in the air gap of $\frac{\lambda}{2} = 0.25$ µm. The 12 fringes over 15 mm correspond to a gap change of $12 \times 0.25 = 3$ µm, so the optical flat is tilted by 3 µm per 15 mm, that is 0.2 µm per mm. The gauges are 45 mm apart, so the height difference is $0.2 \times 45 = 9$ µm.