Lenses

A lens is a combination of two types of transparent surfaces.

When light enters a lens it refracts and the light rays will either diverge or converge. The type of lens used will affect the characteristics of the image formed.

Types of LensesA. Converging Lenses

Three main types:

Biconvex lens

Made from two convex surfaces of equal radii placed back-to-back.

Plano-convex lens

Made from one convex surface and one flat surface.

Positive meniscus lens

Made from two spherical surfaces with different radii. Concave surface + convex surface.

B. Diverging LensesThree main types

Biconcave lens

Made from two concave surfaces of equal radii placed back-to-back.

Plano-concave lens

Made from one concave surface and one flat surface.

Negative meniscus lens

Made from two spherical surfaces with different radii. Convex surface + concave surface.

Ray diagram for lensesParts of a lens.

Converging lens

CV CV

Three principal rays for a converging lens:1.First Principal Ray . If a light ray is parallel to

the principal axis, then it will refract through the focal point, F, of the lens.

2.Second principal ray. If a light ray is moving towards the secondary focal point, F’, it will refract parallel to the principal axis.

3.Third principal ray. A light ray moving towards the optical center, O, will not refract, but continue in a straight line.

F’ O F

Parts of a Diverging Lens:1. Principal focal point , F, is located on the side of the

incident rays.2. Secondary focal point, F’, is a point symmetrical to F

from the optical center, O, of the lens.3. Focal length, f, is distance OF.4. Focal plane is a two dimensional “surface” located

perpendicular to P through F. All parallel incident rays converge here.

F F’O

f

Three principal rays for a diverging lens:1.First Principal Ray . If an incident light ray is

parallel to the principal axis, then the refracted ray travels in a direction in line with the primary focal point, F.

2.Second principal ray. If the incident light ray moves in a direction in line with the secondary focal point, F’, it will refract parallel to the principal axis.

3.Third principal ray. A light ray moving towards the optical center will not refract, but continue in a straight line.

F F’O

Images formed by lenses

Geometric construction

We can use the three principal rays to determine the location and type of image formed by diverging and converging lenses.

Ex. Use the principal rays to locate the image of the arrow formed by the following lenses:

Thin-lens Equation

The characteristics of an image formed with a thin lens can be determined using mathematical relationships.

Thin lens equation:1/f = 1/do + 1/di

Where f is the primary focal point of the lens, do is the distance from the object to the optical

center of the lens, anddi is the distance from the image to the optical center

of the lens.

F’ F

f' f

dodi

Oobject

image

The magnification of an image is determined using :

M = hi/ho = - di/do

Where hi is the image height and

ho is the object height.

Sign convention

As with mirrors, the sign associated with a distance or height gives valuable information on the image’s characteristics.

• Virtual distances are negative. Real distances are positive.

• Inverted images have negative heights. Upright images have positive heights.

• The magnification for an inverted image is negative.

Example 1

A 4 cm object is placed 10 cm from a converging lens whose focal length is 5 cm.

Determine:a)The image position, di

b)The magnification, Mc) The image height, hi

Example 2

A 4 cm object is placed 10 cm from a diverging lens whose focal length is 5 cm.

Determine:a)The image position, di

b)The magnification, Mc) The image height, hi