Cardinal Points of Lens

Explore the six cardinal points of a lens—the front and back focal points, front and back principal points, and front and back nodal points—and their focal, principal, and nodal planes.

Explore why the principal planes matter and how a representative thin lens at the principal plane models thick lenses or complex systems with the thin lens equation, using sign conventions.

Understand the effective focal length as the distance from lens to the focal point for rays from infinity, with sign conventions, and see how telephoto lenses exceed the lens length.

Identify the back principal plane (BPP) as the surface where a thick optical system is replaced by a thin lens using its effective focal length and back focal plane.

Learn the difference between back focal length and effective focal length in a thick lens, from back principal plane to back focal point, including vertex and principal plane definitions.

Define the front focal length (FFL) as the distance from the last surface vertex to the front focal point, opposite the back focal length (BFL).

Explore the front principal plane (FPP) and back principal plane, using converging lines and rays from infinity to locate each plane, which may lie anywhere to simplify the optical system.

Review distance and planes in lens systems, identify back focal length, front focal length, and the effective focal length, and locate the back principal plane and the principal points.

Identify the hiatus of a lens as the separation between the two principal planes in a thick or thin lens, with unitary magnification and unchanged ray height.

Determine the principal planes and effective focal length of a thick lens. Compute h1 and h2 from vertex to principal planes and relate R1, R2, and D to focal positions.

Determine front and back focal lengths for a thick lens using the effective focal length and principal planes, subtracting h1 and h2 to obtain each focal length.

Compute the thick lens effective focal length using radii of curvature, thickness, and refractive index; the example yields 75 mm and back focal length from the back principal plane.

Explore cardinal points of lens by calculating the back principal plane and the effective focal length, with h two negative indicating direction from the surface.

Use the effective focal length of 75 millimeters and the h1 equation to locate the front principal plane with h1 equal to 25, 25 units from the front vertex.

Compute back focal length from the effective focal length and H2 with the equation back focal length equals effective focal length minus absolute value of H2; result 62.5 mm.

Calculate the front focal length from the effective focal length and H1 using the sign convention; the equation yields 50 millimeters.

Review example 1 shows calculating effective focal length, back and front focal lengths using surface radii and refractive index, then explains Zmax methods for locating principal and focal planes.

Learn to add surfaces in Zemax by building a two-surface lens with a stop, set radii, thickness, and a 1.5 index material, and analyze marginal ray height for focus.

Explore how to determine lens cardinal points using Zmax, viewing focal lengths, principal planes, and nodal planes from the first surface, image space, and dummy surfaces.

Define immersed optical system as an optical path inside a liquid such as oil or water. It increases numerical aperture with immersion microscopy, tir e f m, and eye imaging.

Compute the effective focal length of an immersed thick lens by modeling it as two lenses at distance d, using 1/f1 + 1/f2 − d/(n f1 f2) and sign conventions.

Explain immersed optical systems by computing effective focal lengths and principal planes for thick lenses, showing front and back focal lengths, h1 and h2, depend on n and n prime.

Calculate the effective focal length of an immersed thick lens using the focal-length equation, sign conventions, and given radii of curvature, lens thickness, and refractive indices 1.33 and 1.5.

Compute the back principal plane of a lens by applying the effective focal length equations with n2 and f, and determine H2's sign and direction relative to the surface.

Compute the front principal plane of immersed lens by using n1, f, and R2 to obtain an 89.82 mm effective focal length, locating the plane 39.82 units from the surface.

Compute the back focal length from n times the effective focal length minus h2, using the back principal plane. Compare with zmax and the front principal plane h1 for verification.

Calculate front focal length and effective focal length of a lens using the provided equations, with n1, n, h1, and R2, and compare results.

Review example two shows how to reference principal planes and focal planes from the lens front surface, interpret sign changes, and relate back focal planes, back principal planes, and zmax.

Explore adding surfaces in Zemax to build an immersed optical system, using water and glass indices, radii of curvature and thickness, and prepare for calculating the lens cardinal points.

Analyze prescription data for a lens system, comparing left and right focal lengths, effective focal length, and the principal and nodal planes using the imaging surface as reference.

Explore nodal points in lenses, defined by rays exiting at the same angle to the optical axis, and relate them to principal points for practical imaging and magnification behavior.

Identify the mirror's nodal points by tracing rays that pass through the point and reflect back with the same angle, and note that principal planes differ from nodal points.

Identify the nodal points and their meaning; the nodal shift from the principal points equals delta n times the effective focal length, with delta n = n3 - n1.