In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5 . 25 mm and apparent thickness o

Question

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5 . 25 mm and apparent thickness of the glass slab at 5 . 00 mm . Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on Vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is x 10 × 10 - 3 , where x is ______

TestHub · Accepted Answer

Given: 50 V S D = 49 M S D ⇒ 1 V S D = 49 50 M S D So least count will be = 1 M S D - 1 V S D = 1 20 cm - 49 50 · 1 20 cm = 1 50 × 1 20 cm = 0 . 01 mm As we know, μ = h h ' = 5 . 25 5 . 00 Applying log on both sides, we get l n μ = l n h – l n h ’ Differentiating both sides, we get d μ μ = d h h - d h ' h ' For calculation, all errors will be added, therefore d μ = 0 . 01 5 . 25 + 0 . 01 5 . 00 μ = 41 10 × 10 - 3 Hence, x = 41

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