Question

In the measurement of the angle of a prism using a spectrometer, the readings of first reflected image are Vernier $I : 320^\circ 40';$ Vernier $ II : 140^\circ 30' $ and those of the second reflected image are Vernier $ I : 80^\circ 38'; $ Vernier $ II : 260^\circ 24'.$ Then the angle of the prism is

• A. $59^{\circ} 58'$
• B. $59^{\circ} 56'$
• C. $60^{\circ} 2'$
• D. $60^{\circ} 4'$

Answer 1

The Correct Option is A

Angle of the prism,
$ A = \frac{\phi}{2}$
Now $\phi = \frac{\phi_1 +\phi_2}{2}$
Where $ \phi_1 = x_2 - x_1$
$ = (360^\circ + 80^\circ 38')-(320^\circ 40')$
$ = 119^\circ 58' $
and $\phi_2 = y_2 - y_1$
$ = 260^\circ 24' - 140^\circ 30'$
$ = 119^\circ 54' $
$ \phi = \frac{119^\circ 58'+ 119^\circ 54'}{2}$
$ = \frac{239^\circ 52'}{2}$
$ A =\frac{\phi }{2}= \frac{239^\circ 52'}{4}=59^\circ 58'$