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A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading :58.5 degree
Vernier scale reading : 09 divisions
Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

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58.59 degree

58.77 degree

58.65 degree

59 degree

answer is C.

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Detailed Solution

$30 V . S . D \to 29 M . S . D 1 V . S . D \to \frac{29}{30} M . S . D = \frac{29}{30} \times 0.5$

Least count of vernier =1 MS.D – 1 V.S .D

$= {0.5}^{0} - \frac{29}{30} \times {0.5}^{0} = \frac{{0.5}^{0}}{30}$

Reading of vernier =M.S reading + V.S reading $\times$ least count

$= {58.5}^{0} + 9 \times \frac{{0.5}^{0}}{30} = 58.65$

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