1. RAY OPTICS
Reflection of light

2. Rectilinear propagation
Three effects of rectilinear propagation of light
● Formation of shadow.
● Formation of day and night.
● Formation of image from a pinhole camera.
The rectilinear propagation of light means that light travels in straight line

3. Reflection of light
• The two laws of reflection are:
(i) the incident ray, the reflected ray and the normal (at the point of
incidence), all lie in the same plane.This plane is known as plane of
reflection.
(ii) the angle of incidence (i) is always equal to the angle of reflection (r)
∠i = ∠r
R
i
r
• Reflection of light is the phenomenon of bouncing back of light in the same medium on
striking the surface of any object.

4. Types of reflections
Basis of classification: The nature of reflection depends on the smoothness of the
surface.
Regular reflection: The reflection by these smooth surfaces.
Irregular / Diffused reflection: Most of the objects in the everyday world are not smooth
on the microscopic level. The rough surfaces of these objects reflect the rays of light in
many directions. Such reflection is called irregular reflection.

5. Reflection by plane mirrors
If the reflecting surface of the mirror is flat
then we call this type of mirror as plane
mirrors.
image of object formed is always virtual.
The distance of the object to the mirror(u)
is always equal to the distance of the
image to the mirror(v)
The size of the object is always equal to
size of the the image
The lateral inversion is observed in the
case of plane reflection

6. Pair of mirrors placed
at an angle For θ =75
value of 360/θ
360/θ=360/75=4.8
4 is a even no
Then n=360/θ-1=
360/75-1=4.8-1=3.8
No of complete
images formed = 3

7. Deviation by a plane mirror & 2 mirrors inclined to each other
The deviation is δ= (π-2Ө); When we plot a graph we observe at i=0=>δ =π,(max)
Which means that deviation is independent of either
Angle of incidence & reflection it depends on angle
between the mirrors alone

8. Rotation of plane mirror
According to the law of rotation of the mirror, if the mirror is rotated by an angle ‘i’ in clockwise
direction then the reflected ray is rotated by an angle ‘2i‘ in anticlockwise direction.

9. Velocity of object and that of image
Vo=2j &Vi=2j
Vo= 2 cos Өi+2 sin Өj
Vi=-2 cos Өi+2 sin Өj

10. Mirror under motion
Assume the object is at a distance of d from the mirror
and an image is formed at the same distance d on the
other side of the mirror
When the mirror is moving towards the object with a
speed of 2m/s
After a second the new position of the mirror is 2m from
its original position towards the object
The new distance between the object and the mirror is
d-2 so the new image is formed at a distance of d-2
from the mirror on the other side of the mirror
Thus the shift produced in the image position is 4m
Thus if mirror moves with a velocity
of v the image would move with a
velocity of 2v in the same direction

11. If both object and the mirror are in motion
Thus the resultant velocity of the mirror is (4i-1i)=3im/s;
i.e the image will move in the direction of the mirror
and image
If the object & the mirror are moving -2i m/s & -1i m/s
then the resultant velocity of the image is ____
The image will have a velocity of -2i m/s due to object
& 2m/s due to mirror so finally the image doesn’t
If the object & the mirror are moving in the same
direction with speeds 1i m/s & 2i m/s
The image will move -1i m/s,in direction towards the
mirror and 4i m/s,away from the mirror

12. Spherical mirror
A curved mirror is a mirror with a curved reflecting
surface.Most curved mirrors have surfaces that are
shaped like part of a sphere, but other shapes are
sometimes used in optical devices.
Center of Curvature : The point in the centre of the
mirror that passes through the curve of the mirror
and has the same tangent and curvature at that point.
Radius of Curvature : It’s the linear distance between
Pole and the Center of curvature.
Principal axis : The imaginary line passing through
the optical center and the center of curvature of any
lens or a spherical mirror.
Pole : The midpoint of the spherical mirror.

13. Aperture : An aperture of a mirror or lens is a point from
which the reflection of light actually happens. It also gives
the size of the mirror.
Principal Focus : Principal Focus can also be called Focal
Point. It’s on the axis of a mirror or lens wherein rays of light
parallel to the axis converge or appear to converge after
reflection or refraction
.Focus : It’s any given point, where light rays parallel to the
principal axis, will converge after getting reflected from the
mirror.
Spherical mirrors are of two types and they are classified as
follows:
Concave Mirror
Convex Mirror

14. Sign convention
Sign in the case of concave mirror:
Object is always placed in front of the mirror
hence object distance is taken as negative.
The centre of curvature and focus lie in front of
the concave mirror, so radius of curvature and
focal length are taken as negative in the case of
concave mirror.
When image is formed in front of the mirror, the
distance of image is taken as – (negative) and
when image is formed behind the mirror, the
distance of image is taken as + (positive).
Height of image is taken as positive in the case
of erect image and taken as negative in the case
of inverted image.
Sign is taken as + (positive) behind the
spherical mirror.
Sign is always taken as – ( negative) in
front of a spherical mirror
The height of is taken as + (positive) above
the principal axis and taken as – (negative)
below the principal axis.

15. Sign convention
Sign in the case of a convex mirror:
Object is always placed in front of the mirror
hence object distance is taken as negative.
The centre of curvature and focus lies behind
the convex mirror, so radius of curvature and
focal length are taken as + (positive) in the
case of convex mirror.
Image always formed behind the mirror, thus
the distance of image is taken as positive.
In the case of a convex mirror, always an
erect image is formed, thus the height of
image is taken as positive.

16. Rules for Ray Diagrams for Concave Mirrors
Rule 1
Incident light rays that are parallel to the principal axis will
pass through the focal point after reflecting off the mirror.
Rule 2
Incident light rays that pass through the focal point will
become parallel to the principal axis after reflecting off the
mirror. (This is the reverse concept of rule 1.)

17. Rule 3
Light ray passing through the centre of curvature will
retrace it’s path after reflection.
Rule 4
Ray incident at pole is reflected back making same
angle with the principal axis

18. Rules for Ray Diagrams for Convex Mirrors
Rule 1
Incident light rays that are parallel to the principal axis
will pass through the focal point after reflecting off the
mirror.
Rule 2
Incident light rays that pass through the focal point will
become parallel to the principal axis after reflecting off
the mirror. (This is the reverse concept of rule 1.)

19. Rule 3
Light ray passing through the centre of curvature
will retrace it’s path after reflection.
Rule 4
Ray incident at pole is reflected back making
same angle with the principal axis

20. Object at
infinity
Image at F
real,inverted,
& point sized
image
Object between
infinity & C
Image between C
& F
real,inverted&
diminished image
Object at C
Image at C
Real,inverted & same
sized image
Object between C & F
Image between C & infinity
Real,inverted & enlarged
image

21. Object at F
Image at
infinity
real,inverted
& highly
enlarged
image
Object between F
& P
Image on the other
side of the mirror
virtual,erect&
enlarged image
Convex mirror Object at infinity
Image at F
Erect,virtual &
point sized
Object infront of the mirror; image between F & P
Virtual,erect & diminished

22. Mirror equation
The figure shows an object AB at a distance ‘u’ from the pole
of a concave mirror. The image A1B1 is formed at a distance
‘v’ from the mirror. The position of the image is obtained by
drawing a ray diagram.
Consider the triangles A1CB1 and ACB

24. Relation between m,u,v & f
Magnification, m = – v/u
Mirror formula is 1/f = 1/v + 1/u
Multiplying v on both sides
1+v/u=v/f
v/u=v/f-1
v/u=(v-f)/f
m=-v/u
m=-(v-f)/f=(f-v)/f
m=(f-v)/f
Magnification, m = – v/u
Mirror formula is 1/f = 1/v + 1/u
Multiplying u on both sides
u/f=u/v+1
u/v=u/f-1=u/f - f/f
u/v=(u-f)/f
v/u=f/(u-f)
m=- v/u= f / (f-u)

28. An inverted image is magnified by 2 when the object is placed 22 cm in front of a
concave mirror. Determine the image distance and the focal length of the mirror.
Determine the image distance and image height for a 5.00-cm tall object placed 30.0
cm from a concave mirror having a focal length of 15.0 cm.
A magnified, inverted image is located a distance of 32.0 cm from a concave mirror with
a focal length of 12.0 cm. Determine the object distance and tell whether the image is
real or virtual.
A converging mirror forms a real image of height 4 cm, of an object of height 1 cm
placed 20 cm away from the mirror. Calculate the image distance. What is the focal
length of the mirror?
An arrow 2.5 cm high is placed at a distance of 25 cm from a diverging mirror of focal
length 20 cm., Find the nature, position and size of the image formed.

29. 1.A convex mirror of focal length f forms an image which is 1/n times the object. The
distance of the object from the mirror is
a.(n-1)f b.(n-1/n) f c.(n+1/n) f d.(n+1) f
2.The focal length of a concave mirror is f and the distance from the object to the
principal focus is x. The ratio of the size of the image to the size of the object is
a) (f + x)/f b)f/x c)f2/x2 d)f2/x
3.In a concave mirror experiment, an object is placed at a distance x1 from the focus and
the image is formed at a distance x2 from the focus. The focal length of the mirror would
be a)x1x2 b)(x1+x2)/2 c)√x1x2
d)√x1/x2
4.A square wire of side 3.0 cm is placed 25 cm in front a concave mirror of focal length
10cm with its centre on the axis of the mirror and its plane normal to the axis. The area
enclosed to the Image of the wire is a.7.5cm2 b.6.0cm2 c.4.0cm2
d.3.0cm2