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

Units and Measurements PYQ — JEE Main 2012 · Shift 0 · Q68 with Solution

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Correct answer: C

Given data
- Main scale reading (MSR) $= 58.5^\circ$
- Vernier scale reading $= 9$ divisions
- $1$ main scale division (MSD) $= 0.5^\circ$
- $30$ vernier scale divisions (VSD) $= 29$ main scale divisions (MSD)
Find the value of 1 vernier scale division

Since $30\,\text{VSD} = 29\,\text{MSD}$ and $1\,\text{MSD} = 0.5^\circ$

therefore, $30\,\text{VSD} = 29 \times 0.5^\circ = 14.5^\circ$

So, $1\,\text{VSD} = \frac{14.5^\circ}{30} = 0.4833^\circ$
Find the least count

For a direct vernier, $\text{Least Count} = 1\,\text{MSD} - 1\,\text{VSD}$

$= 0.5^\circ - 0.4833^\circ = 0.0167^\circ$

Thus, $\text{LC} = \frac{1}{60}^\circ$
Vernier contribution

Given vernier coincidence = $9$ divisions,

$\text{Vernier reading} = 9 \times \text{LC} = 9 \times 0.0167^\circ = 0.15^\circ$
Total reading

$\text{Total angle} = \text{MSR} + \text{Vernier reading}$

$= 58.5^\circ + 0.15^\circ = 58.65^\circ$
Match with options
- A: $58.59^\circ$
- B: $58.77^\circ$
- C: $58.65^\circ$ ✅
- D: $59^\circ$

Hence, the correct answer is Option C.