Question
Describe spherical aberration for spherical lenses. What are different ways to minimize or eliminate it?
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Answer
i. All the formulae used for image formation by lenses are based on some assumption. However, in reality these assumptions are not always true.ii. A single point focus in case of lenses is possible only for small aperture spherical lenses and for paraxial rays.
iii. The rays coming from a distant object farther from principal axis no longer remain parallel to the axis. Thus, the focus gradually shifts towards pole.
iv. This defect arises due to spherical shape of the refracting surface, hence known as spherical aberration. It results into a blurred image with unclear boundaries.
v. As shown in figure, the rays near the edge of the lens converge at focal point $F_M$. Whereas, the rays near the principal axis converge at point $F_P$. The distance between $F_M$ and $F_P$ is measured as the longitudinal spherical aberration.
vi. In absence of this aberration, a single point image can be obtained on a screen. In the presence of spherical aberration, the image is always a circle.
vii. At a particular location of the screen (across AB in figure), the diameter of this circle is minimum. This is called the circle of least confusion. Radius of this circle is transverse spherical aberration.
Methods to eliminate/reduce spherical aberration in lenses:
i. Cheapest method to reduce the spherical aberration is to use a planoconvex or planoconcave lens with curved side facing the incident rays.
ii. Certain ratio of radii of curvature for a given refractive index almost eliminates the spherical aberration. For $n = 1.5$, the ratio is
$\frac{R_1}{R_2}=\frac{1}{6}$ and for $n =2, \frac{R_1}{R_2}=\frac{1}{5}$
iii. Use of two thin converging lenses separated by distance equal to difference between their focal lengths with lens of larger focal length facing the incident rays considerably reduces spherical aberration.
iv. Spherical aberration of a convex lens is positive (for real image), while that of a concave lens is negative. Thus, a suitable combination of them can completely eliminate spherical aberration.
iii. The rays coming from a distant object farther from principal axis no longer remain parallel to the axis. Thus, the focus gradually shifts towards pole.
iv. This defect arises due to spherical shape of the refracting surface, hence known as spherical aberration. It results into a blurred image with unclear boundaries.
v. As shown in figure, the rays near the edge of the lens converge at focal point $F_M$. Whereas, the rays near the principal axis converge at point $F_P$. The distance between $F_M$ and $F_P$ is measured as the longitudinal spherical aberration.
vi. In absence of this aberration, a single point image can be obtained on a screen. In the presence of spherical aberration, the image is always a circle.
vii. At a particular location of the screen (across AB in figure), the diameter of this circle is minimum. This is called the circle of least confusion. Radius of this circle is transverse spherical aberration.
Methods to eliminate/reduce spherical aberration in lenses:
i. Cheapest method to reduce the spherical aberration is to use a planoconvex or planoconcave lens with curved side facing the incident rays.
ii. Certain ratio of radii of curvature for a given refractive index almost eliminates the spherical aberration. For $n = 1.5$, the ratio is
$\frac{R_1}{R_2}=\frac{1}{6}$ and for $n =2, \frac{R_1}{R_2}=\frac{1}{5}$
iii. Use of two thin converging lenses separated by distance equal to difference between their focal lengths with lens of larger focal length facing the incident rays considerably reduces spherical aberration.
iv. Spherical aberration of a convex lens is positive (for real image), while that of a concave lens is negative. Thus, a suitable combination of them can completely eliminate spherical aberration.
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