Question

I must design an optical system with an effective focal length between 100 and 300 mm. I should pick the focal length, and it should not be an integer value. The front principal plane should be to the right of the last element, and the rear principal plane should be to the left of the first element. We will start with thin lenses and then turn this into a system with thick lenses. where this condition must be met, so you’ll want some margin in your thin lens design. Object space, image space, and intermediate optical spaces can be any index that satisfies 1.0 ≤ n ≤ 1.8.

First, we will design the system with thin lenses. We must have at least 2 and at most 4. The spacings must all be realizable. In other words, we can’t have the second lens to the left of the first lens. Another way to state this is that the order in which light encounters each lens should be what would happen if we built your system. A different way to say the same thing is that the directed distance from lens 1 to lens 2 must be positive. The required distance from lens 2 to lens 3 must be positive. We need to find: • What is the effective focal length of your system (which means no afocal relays) • What focal length thin lenses did you use • What is the spacing between the thin lenses • What indices did you use • Where is the front principal plane • Where is the rear principal plane • Where is F • Where is F’ We can only use Gaussian reduction for this part; you'll need to show your work.

Answer 1

When designing an optical system with thin lenses, one must use the thin lens equation to find suitable focal lengths and spacings, ensuring realizable distances and correct placement of the principal planes. The magnification is related to focal lengths and object distances. These parameters are crucial in transforming the design of a system with thick lenses.

Step-by-step explanation:

Designing an optical system with thin lenses involves using the thin lens equation to determine the focal lengths and spacing of lenses, constrained by physical and optical principles. When using a plano-convex lens, such as the one with a radius of curvature R₂ = -35 cm and an index of refraction of 1.5, we apply the lensmaker's equation to find its focal length. For any optical system, the focal lengths of individual lenses, the object distance (do), the image distance (di), and the indices of refraction for each space must be considered to ensure a real image.

In designing a system with more than one lens, the effective focal length of the combination can be found by considering the focal lengths and spacing between lenses. The principal planes and the focal points (F and F') are also determined by these factors, adhering to the rule that directed distances must be positive to have a realizable physical system. Additionally, magnifications, represented by 'm', can be computed from the focal lengths and object distances, providing insight into the size and orientation of the resulting image.

The process involves selecting non-integer focal lengths within the specified range, ensuring the positioning of the principal planes as needed, and optimizing the spacings between lenses to meet the system's requirements while considering the margins required when converting to a thick lens system. By harnessing Gaussian reduction techniques, we can create a simplified model before incorporating the complexities associated with thick lenses into the design.