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Which of the following quantities relate...

Which of the following quantities related to a lens depend on the wavelength or wavelengths of the incident light?
(Choose the incorrect option)

A

a.power

B

b.focal length

C

c.chromatic aberration

D

d.radii of curvature

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze each of the options given and determine which quantity related to a lens does not depend on the wavelength of light. ### Step-by-Step Solution: 1. **Understanding Focal Length**: - The focal length (F) of a lens is related to the refractive index (μ) of the lens material. The refractive index is known to vary with the wavelength of light (λ). - The relationship can be expressed as: \[ F \propto \frac{1}{\mu} \] - Since μ depends on λ, it follows that the focal length also depends on the wavelength of light. 2. **Analyzing Power**: - Power (P) of a lens is defined as the reciprocal of the focal length: \[ P = \frac{1}{F} \] - Since F depends on λ, it implies that power also depends on the wavelength of light. Thus, power is also affected by the wavelength. 3. **Chromatic Aberration**: - Chromatic aberration occurs due to the variation of the refractive index with different wavelengths of light. - Different wavelengths will focus at different points due to their varying speeds in the lens material, leading to color fringing. - Therefore, chromatic aberration is also dependent on the wavelength of light. 4. **Radii of Curvature**: - The radii of curvature (R) of the lens surfaces are physical dimensions and do not change with the wavelength of light. - The radii of curvature are fixed properties of the lens and are independent of the light's wavelength. 5. **Conclusion**: - From the analysis, we find that the quantities that depend on the wavelength of light are: - Focal Length (F) - Power (P) - Chromatic Aberration - The quantity that does not depend on the wavelength of light is the **Radii of Curvature**. ### Final Answer: The incorrect option is **Radii of Curvature**. ---
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