Mirror and Lens

by Rifki Irawan

a surface, such as polished metal or glass coated with a metal film, that reflects light without diffusion and produces an image of an object placed in front of it

Mirror Lensa piece of glass or other transparent material, used to converge or diverge transmitted light and form optical images

convex and concave

concave mirror convex mirror

If the mirror coating is in the inside of the spherical surface, then the mirror is

called a convex mirror

If the mirror coating is on the outside of the spherical surface, then the mirror is

called a concave mirror

C C

center of curvature

center of curvature

hollow sphere of glass

principal axis

radius of curvature

R

radius of curvature

R

Pole (P)

F F

Center of curvature : the center of the hollow sphere from which the mirror has been cut. It is represented by the letter C.

It can be observed that C of a convex mirror is behind the mirrored surface. On the other hand, C for a concave mirror is in front of the mirror.

Principal axis of the mirror :A straight line that passes through the center of curvature (C )and the pole (P) of the mirror, is called the principal axis of the mirror.

Focal Length of a mirror :When parallel rays of light coming from an infinite distance, fall on either a concave or a convex mirror, they are reflected back to a point on the principal axis.

C F

The light (ray) properties of concave mirrorAny light ray traveling parallel to the principal axis is reflected by the curved mirror through the principal focus.Any light ray that passes through the principal focus is reflected by the curved mirror parallel to the principal axis.Any light ray that passes through the center of curvature retraces its initial path after reflection by the curved mirror.

the object is between infinity and the center of curvature in front of a concave mirror

C F

The images properties of concave mirror

• The image is real.• The image is inverted.• The image is diminished.• The image is formed between the principal focus and

the center of curvature in front of the concave mirror.

C F

CF

the object is anywhere in front of a convex mirror

CF

The images properties of convex mirror

• The image is virtual.• The image is upright.• The image is diminished.• The image is formed between the pole and

principal focus behind the convex mirror.

1. When the object is at infinity in the case of a concave mirror

2. When the object is placed at the center of curvature in front of a concave mirror

3. When the object is placed between the principal focus and the center of curvature in front of a concave mirror

4. When the object is placed at the principal focus in front of a concave mirror

5. When the object is placed between the pole and the principal focus in front of a concave mirror

The images properties of convex mirror

When the object is at infinity in the case of a convex mirror, the image formed has the following characteristic properties.

1. The image is virtual.2. The image is upright.3. The image is highly diminished to a point.4. The image is formed at the principal focus behind the convex mirror. When the object is anywhere between the pole and infinity in front of a convex mirror, the image formed has the following characteristic properties.

5. The image is virtual.6. The image is upright.7. The image is diminished.8. The image is formed between the principal focus and the pole behind the convex

mirror.

Anatomy of the lens

A piece of glass or transparent materials that can converges and diverges rays

from a point is referred to a lens.

Lens

Converging Lens Diverging Lensconverges rays of light which are

traveling parallel to its principal axisdiverges rays of light which are

traveling parallel to its principal axis

relatively thick across their middle and thin at their upper and lower

edges

relatively thin across their middle and thick at their upper and lower

edges

Converging lens

F

Diverging lens

F

Vertical Axis

Principal Axis

F F 2F2F

focallength

Thin Converging lens

F F 2F2F

+

Ray (diagonal line) from the object passing through the centre of the lens

Ray 1

Ray parallel to the principal axis and after coming out from the lens, passes through the focal point

Ray 2

Ray passes through the focal point and after coming out from the lens, parallel with the principal axis

Ray 3

F F 2F2F

+

+

18 cm 6cm

A

An object (A) 6 cm high placed 18 cm in front of a positive lens of focal length 6 cm. Draw the diagram to scale and by tracing the paths of rays from A, find the position and size of the image formed.

The linear magnification m is given by

m = height of image (hi)

height of object (ho)

m = distance of image to the lens / mirror (si)

distance of object to the lens / mirror (so)

hi

ho

si

so= Power of lens (P) = 1

f

1si

+1so

=1f