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4. The GRIN Slab as a Lens. Show that a SELFOC slab of length d < π/2α and with a refractive index distribution n^2(y) = n0^2(1 – α^2y^2) acts as a cylindrical lens (a lens with focussing power in the y-z plane) of focal length f ≈ 1/n0α sin(αd) Show that the principal point (defined in Figure 4.1) lies at a distance from the slab edge AH ≈ (1/n0α) tan(αd/2). Sketch the ray trajectories in the special cases d = π α and d = π/2α. Figure 4.1: The SELFOC slab used as a lens; F is the focal point and H is the principal point.

4. The GRIN Slab as a Lens. Show that a SELFOC slab of length d < π/2α and with a refractive index distribution n^2(y) = n0^2(1 – α^2y^2) acts as a cylindrical lens (a lens with focussing power in the y-z plane) of focal length f ≈ 1/n0α sin(αd) Show that the principal point (defined in Figure 4.1) lies at a distance from the slab edge AH ≈ (1/n0α) tan(αd/2). Sketch the ray trajectories in the special cases d = π α and d = π/2α. Figure 4.1: The SELFOC slab used as a lens; F is the focal point and H is the principal point.

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4. The GRIN Slab as a Lens. Show that a SELFOC slab of length d < π/2α and with a refractive index distribution n^2(y) = n0^2(1 – α^2y^2) acts as a cylindrical lens (a lens with focussing power in the y-z plane) of focal length f ≈ 1/n0α sin(αd) Show that the principal point (defined in Figure 4.1) lies at a distance from the slab edge AH ≈ (1/n0α) tan(αd/2). Sketch the ray trajectories in the special cases d = π α and d = π/2α. Figure 4.1: The SELFOC slab used as a lens; F is the focal point and H is the principal point.

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I want to ask to show the system is an imaging system and to show the importance of these points by tracing the trajectories of rays that are incident parallel to opical axis.

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