Join 60,000+ competitive exam aspirants
or with email
Your Cart
SubtotalтВ╣0
TotalтВ╣0
Examoogle тАв User тАв info@examoogle.com тАв EE-2024-8821
Chapter 1 of 12 тАв Page 1 of 248ЁЯФТ Protected PDF тАв Watermarked
Join 60,000+ competitive exam aspirants
Which of the following describes the relationship between the aperture of a lens and its radius of curvature in the context of thin lenses?
The aperture is much smaller than the radius of curvature.
The aperture equals the radius of curvature.
The aperture is much larger than the radius of curvature.
The aperture is independent of the radius of curvature.
The aperture is much smaller than the radius of curvature.
In the optics of thin lenses, the aperture (the diameter of the lens) is kept much smaller than the radius of curvature of the spherical surfaces. This design ensures that the rays striking the lens are close to the principal axis, allowing for paraxial approximation and minimizing spherical aberration.
In the optics of thin lenses, the aperture (the diameter of the lens) is kept much smaller than the radius of curvature of the spherical surfaces. This design ensures that the rays striking the lens are close to the principal axis, allowing for paraxial approximation and minimizing spherical aberration.
Think of a camera lens; by keeping the opening (aperture) narrow, the light rays travel through the 'sweet spot' of the glass where the curve is almost flat, resulting in a much sharper, clearer image without distortion at the edges.
rac{1}{f} = (n-1) \left( rac{1}{R_1} - rac{1}{R_2} ight) тАФ The Lens Maker's Formula
rac1f=rac1vтИТrac1u тАФ The Thin Lens Equation
The thin lens approximation assumes the thickness is negligible compared to the radius of curvature R of its surfaces. By keeping the aperture small, the lens ensures that all light rays make small angles with the principal axis (sinhetaтЙИheta). This condition is essential for the validity of the Lens Maker's Formula and thin lens equation, as it suppresses aberrations that occur at wider angles.
Thin lens theory relies on the paraxial approximation, where rays are near the axis.
Small aperture prevents significant spherical aberration.
The radius of curvature is generally defined as much larger than the lens diameter (aperture).
Minimizes spherical aberration
Allows for simplified paraxial ray tracing
Produces sharper images on the focal plane
Small aperture limits the amount of light entering the lens (limiting speed)
Not suitable for high-speed photography which requires large apertures
Corrective eyeglasses
Standard laboratory optical equipment
In geometric optics, 'thin' implies the lens thickness t is significantly smaller than the radius of curvature R and object/image distances.
Option B is incorrect because if the aperture equaled the radius, the lens would be a hemisphere, violating thin-lens assumptions.
Option C is incorrect because a large aperture lens would introduce severe spherical aberration.
A is correct тАФ The aperture must be much smaller than the radius of curvature to satisfy the paraxial approximation and ensure the validity of thin lens formulas.
Always remember that the 'thin lens' approximation is valid only when D<<R and D<<f; if this condition is violated, you must account for higher-order Seidel aberrations.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download тАв 100K+ Aspirants