Question

The reading given by a spectrometer when it is used to measure the angle of a prism is as follows

Main scale reading = 58.5°

Vernier scale reading = 9 divisions

1 division on main scale corresponds to 0.5°

30 is the total division on the vernier scale and it matches with 29 divisions of the main scale.

What is the angle of the prism?

(a) 59°

(b) 58.77°

(c) 58.59°

(d) 58.65°

Answer 1

Correct option is (d) 58.65°

Given, value of main scale = 58.5°

Reading of vernier scale = 9 division

30 vernier scale division (VSD) = 29 main scale division (MSD)

1 VSD = \(\frac{29}{30} \) MSD

Least count = 1 MSD - 1 VSD

= \((1 - \frac{29}{30}) \) MSD

= \( \frac 1{30} \times 0.5°\)

Prism angle = Value of main scale + Reading of vernier scale x Least count

= \(58.5° + 9\times \frac{0.5°}{30}\)

= 58.5° + 0.15°

= 58.65°