Surface Power, Thin Lens & Lens Form

Surface Power

• We now know that the power of a lens is the reciprocal of its focal length, in meters. • Today we’ll look at surface powers and the factors affecting surface power.

Surface Power

• The power of a surface depends on: 1. the curvature of the surface and 2. the refractive index of the material.

Curvature

• If we consider that the surface of the lens is a part of a circle. The centre of the circle is referred to as the centre of curvature (C). • The radius of curvature is the radius of the circle and is measured from the surface of the lens to the centre of curvature.

Radius of curvature (r) Centre of Curvature (C)

Curvature

• The curvature of the surface (R), in Dioptres, is related to the radius of curvature of the surface in meters (r). • The greater the radius of curvature the flatter the surface, and the smaller the curvature. R=1 r

2. Refractive Index

• The ratio between the speed of light in air and its speed in a particular medium is called it’s refractive index. Refractive index = velocity of light in air velocity of light in medium Refractive index = n

Convex Surface

F (D)

r (m) Optic axis C

n

n’

In this case, using the sign convention, the radius of curvature will be positive (radius is measured from the surface to the centre of curvature)

Concave Surface

F (D)

r (m) Optic axis C n n’

In this case, using the sign convention, the radius of curvature will be negative (radius is measured from the surface to the centre of curvature)

• So: F = n’ – n F = Dioptres r r = metres • Remember: “refractive index of the medium which the light is about to enter minus the refractive index of the medium which the light is leaving”

Thin Lens

• A lens has two surfaces separated by a thickness of glass. • For now, we’ll assume the lens to be thin. • So, the first surface is F1 and the second surface is F2. • Hence, the total power of a thin lens will simply be...

Surface Power

• We now know that the power of a lens is the reciprocal of its focal length, in meters. • Today we’ll look at surface powers and the factors affecting surface power.

Surface Power

• The power of a surface depends on: 1. the curvature of the surface and 2. the refractive index of the material.

Curvature

• If we consider that the surface of the lens is a part of a circle. The centre of the circle is referred to as the centre of curvature (C). • The radius of curvature is the radius of the circle and is measured from the surface of the lens to the centre of curvature.

Radius of curvature (r) Centre of Curvature (C)

Curvature

• The curvature of the surface (R), in Dioptres, is related to the radius of curvature of the surface in meters (r). • The greater the radius of curvature the flatter the surface, and the smaller the curvature. R=1 r

2. Refractive Index

• The ratio between the speed of light in air and its speed in a particular medium is called it’s refractive index. Refractive index = velocity of light in air velocity of light in medium Refractive index = n

Convex Surface

F (D)

r (m) Optic axis C

n

n’

In this case, using the sign convention, the radius of curvature will be positive (radius is measured from the surface to the centre of curvature)

Concave Surface

F (D)

r (m) Optic axis C n n’

In this case, using the sign convention, the radius of curvature will be negative (radius is measured from the surface to the centre of curvature)

• So: F = n’ – n F = Dioptres r r = metres • Remember: “refractive index of the medium which the light is about to enter minus the refractive index of the medium which the light is leaving”

Thin Lens

• A lens has two surfaces separated by a thickness of glass. • For now, we’ll assume the lens to be thin. • So, the first surface is F1 and the second surface is F2. • Hence, the total power of a thin lens will simply be...