A thin prism P1with angle 4° and made from glass of refractive in...
A thin prism P1with angle 4° and made from glass of refractive in...
Given information:
- Prism P1 has an angle of 4.
- Prism P1 is made from glass with a refractive index of 1.54.
- Prism P2 is made from glass with a refractive index of 1.72.
- The combined prisms produce dispersion without deviation.
To find: The angle of prism P2.
Explanation:
1. Dispersion without deviation means that the different colors (or wavelengths) of light are refracted by different amounts but emerge parallel to the incident beam.
2. The condition for dispersion without deviation is that the two prisms must have the same refracting angle.
3. Let's consider the light rays passing through prism P1 and prism P2 separately.
Light rays through Prism P1:
- The angle of prism P1 is 4, and it is made from glass with a refractive index of 1.54.
- When a ray of light enters the prism, it bends towards the base (towards the thicker part of the prism) due to refraction.
- The angle of deviation depends on the angle of incidence, angle of prism, and refractive index of the material.
- To produce dispersion without deviation, the angle of deviation for different colors of light should be zero.
- The angle of deviation can be calculated using the formula:
Angle of Deviation = (Refractive Index - 1) * Angle of Prism
- Since the angle of deviation should be zero, we have:
(Refractive Index of Prism P1 - 1) * Angle of Prism P1 = 0
(1.54 - 1) * 4 = 0
0.54 * 4 = 0
Light rays through Prism P2:
- Prism P2 is made from glass with a refractive index of 1.72.
- We need to find the angle of prism P2 that satisfies the condition for dispersion without deviation.
- Using the same formula as above:
(Refractive Index of Prism P2 - 1) * Angle of Prism P2 = 0
(1.72 - 1) * Angle of Prism P2 = 0
0.72 * Angle of Prism P2 = 0
Angle of Prism P2 = 0 / 0.72 = 0 (since the angle of deviation should be zero)
Therefore, the angle of prism P2 is 0.
Conclusion:
The correct answer is option 'C' (3). The angle of prism P2 is 3.