Concepts Of Physics MCQ Edition [Volume 1]
- Exam
- Concepts Of Physics MCQ Edition [Volume 1]
- Subject
- Physics
- Chapter
- Dispersion and Spectra
Concepts Of Physics MCQ Edition [Volume 1] · Physics · Dispersion and Spectra
Two thin prisms, one of crown glass ( μ_r = 1.515 , μ_v = 1.525 )...
Two thin prisms, one of crown glass (, ) and the other of flint glass (, ), are positioned in contact. Each has a refracting angle of 5.0^{}^{{}^{\circ}} and they are oriented in the same direction. Compute the angular dispersion generated by this combination.
Options
- A0.10^{}^{{}^{\circ}}
- B0.20^{}^{{}^{\circ}}
- C0.15^{}^{{}^{\circ}}
- D0.05^{}^{{}^{\circ}}
Correct answer
C. 0.15^{}^{{}^{\circ}}
Step-by-step solution
The angular dispersion produced by a thin prism is given by .
For the crown glass prism:
\theta_1 = (1.525 - 1.515) \times 5.0^{}^{{}^{\circ}} = 0.010 \times 5.0^{}^{{}^{\circ}} = 0.05^{}^{{}^{\circ}}
For the flint glass prism:
\theta_2 = (1.632 - 1.612) \times 5.0^{}^{{}^{\circ}} = 0.020 \times 5.0^{}^{{}^{\circ}} = 0.10^{}^{{}^{\circ}}
Since the prisms are oriented in the same direction, their angular dispersions add up.
Total angular dispersion \theta = \theta_1 + \theta_2 = 0.05^{}^{{}^{\circ}} + 0.10^{}^{{}^{\circ}} = 0.15^{}^{{}^{\circ}}
For the crown glass prism:
\theta_1 = (1.525 - 1.515) \times 5.0^{}^{{}^{\circ}} = 0.010 \times 5.0^{}^{{}^{\circ}} = 0.05^{}^{{}^{\circ}}
For the flint glass prism:
\theta_2 = (1.632 - 1.612) \times 5.0^{}^{{}^{\circ}} = 0.020 \times 5.0^{}^{{}^{\circ}} = 0.10^{}^{{}^{\circ}}
Since the prisms are oriented in the same direction, their angular dispersions add up.
Total angular dispersion \theta = \theta_1 + \theta_2 = 0.05^{}^{{}^{\circ}} + 0.10^{}^{{}^{\circ}} = 0.15^{}^{{}^{\circ}}