Question

Using a suitable ray diagram, establish a relation between radius of curvature and focal
of a convex lens for paraxial rays
2. Using a suitable ray diagram, establish a relation between center of curvature and focal length of a concave lens for paraxial rays.
​

Answer 1

$\rule{200}{2}$

$\huge\boxed{\boxed{\underline{\mathcal{\red{A}\green{N}\pink{S}\orange{W}\blue{E}\pink{R:-}}}}}$

One of the easiest shapes to analyze is the spherical mirror. Typically such a mirror is not a complete sphere, but a spherical cap — a piece sliced from a larger imaginary sphere with a single cut. Although one could argue that this statement is quantifiably false, since ball bearings are complete spheres and they are shiny and plentiful. Nonetheless as far as optical instruments go, most spherical mirrors are spherical caps.

Start by tracing a line from the center of curvature of the sphere through the geometric center of the spherical cap. Extend it to infinity in both directions. This imaginary line is called the principal axis or optical axis of the mirror. Any line through the center of curvature of a sphere is an axis of symmetry for the sphere, but only one of these is a line of symmetry for the spherical cap. The adjective "principal" is used because its the most important of all possible axes. Compare this with the principal of a school, who is in essence the most important or principal teacher. The point where the principal axis pierces the mirror is called the pole of the mirror. Compare this with the poles of the earth, the place where the imaginary axis of rotation pierces the literal surface of the spherical earth.

Imagine a set of rays parallel to the principal axis incident on a spherical mirror (paraxial rays as they are sometimes called). Let's start with a mirror curved like the one shown below — one where the reflecting surface is on the "inside", like looking into a spoon held correctly for eating, a concave mirror.

Answer 2

Answer:

One of the easiest shapes to analyze is the spherical mirror. Typically such a mirror is not a complete sphere, but a spherical cap — a piece sliced from a larger imaginary sphere with a single cut. Although one could argue that this statement is quantifiably false, since ball bearings are complete spheres and they are shiny and plentiful. Nonetheless as far as optical instruments go, most spherical mirrors are spherical caps.

Start by tracing a line from the center of curvature of the sphere through the geometric center of the spherical cap. Extend it to infinity in both directions. This imaginary line is called the principal axis or optical axis of the mirror. Any line through the center of curvature of a sphere is an axis of symmetry for the sphere, but only one of these is a line of symmetry for the spherical cap. The adjective "principal" is used because its the most important of all possible axes. Compare this with the principal of a school, who is in essence the most important or principal teacher. The point where the principal axis pierces the mirror is called the pole of the mirror. Compare this with the poles of the earth, the place where the imaginary axis of rotation pierces the literal surface of the spherical earth.

Imagine a set of rays parallel to the principal axis incident on a spherical mirror (paraxial rays as they are sometimes called). Let's start with a mirror curved like the one shown below — one where the reflecting surface is on the "inside", like looking into a spoon held correctly for eating, a concave mirror.