Light of wavelength 4000 Å is incident at small angle on a prism...
Because this light has only one wavelength. Dispersion takes place in white light not a single wavelength
Light of wavelength 4000 Å is incident at small angle on a prism...
Explanation:
Given data:
- Wavelength of light, λ = 4000 Å
- Apex angle of prism, A = 4°
- Refractive index of prism, np = 1.5
- Refractive index of surrounding medium, nr = 1.48
Calculation:
- The angle of minimum deviation (δm) for a prism is given by the formula:
sin[(A + δm)/2] / sin(A/2) = np/nr
- For small angles of incidence, we can assume that sinδ ≈ tanδ ≈ δ (in radians)
- Therefore, the angle of dispersion (D) produced by the prism is given by:
D = δm - δ = 2δm - A
- Substituting the values in the formula, we get:
sin[(A + δm)/2] / sin(A/2) = np/nr
sin[(4° + δm)/2] / sin(2°) = 1.5/1.48
- Solving the above equation, we get:
δm ≈ 0.192°
Therefore, the angle of dispersion produced by the prism in this light is approximately 0.192°. Hence, the correct answer is option 'D'.