Fermat's principle states that light will travel between two points along the path that takes the least time, as compared to nearby paths. From Fermat's principle, we can derive the laws of reflection and refraction. The law of reflection states that the incident ray, normal, and reflected ray all lie in the same plane and the angles of incidence and reflection are equal. The law of refraction states that the ratio of the sines of the incident and refracted angles is a constant value equal to the refractive index when light passes from one medium to another. Spherical mirrors can be either concave or convex. Concave mirrors can form real or virtual images and have a focal point in front of the mirror. Convex

2. Fermat’s principle:

3. Fermat’s principle:
“light travel b/w two points along the path that required the
least time as compared to other nearby path is called Fermat's
principle”
From Fermat's we determine:
 Law of reflection [i = r ]
 Law of refraction [
sin 𝜃1
sin 𝜃2
=n]

4. When light travel in the certain medium fall on the surface of other medium the part
of it turn back in the certain medium this is called reflection of light
Law of reflection:
 The incident ray, the
normal and the reflected
ray at the point of
incident all lie in the same
plane
 The angle of incident is
equal to the angle of
reflection
Normal
Plane mirror
i = r
𝜃1
𝜃2

5. The process of bending of light when it passes from one medium to other is called
refraction of light.
Law of refraction:
 The incident ray, the
normal and the reflected
ray at the point of
incident all lie in the same
plane
 The ratio of sin of angle
incident and sin of angle
of refraction are always
equal to constant.
Normal
Mirror slab
Normal
sin 𝜃1
sin 𝜃2
=n
𝜃1
𝜃2

6. Law of reflection:
x d-x
𝜃1
𝜃2
p
A
B
a b
d
N
sin𝜃1=
𝑎
𝑎2+𝑥2
sin𝜃2=
𝑑−𝑥
𝑏2+(𝑑−𝑥)2
sin𝜃1=
𝑝𝑒𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑜𝑢𝑠
L= 𝑎2 + 𝑥2 + 𝑏2 + (𝑑 − 𝑥)2
AP= 𝑎2 + 𝑥2
PB= 𝑏2 + (𝑑 − 𝑥)2
L=AP+PB
𝑑𝐿
𝑑𝑥
=
2𝑥
2 𝑎2+𝑥2
+
2(𝑑−𝑥)(−1)
2 𝑏2+(𝑑−𝑥)2
𝑑𝐿
𝑑𝑥
=0
0=
2𝑥
2 𝑎2+𝑥2
+
2(𝑑−𝑥)(−1)
2 𝑏2+(𝑑−𝑥)2
0=
𝑥
𝑎2+𝑥2
-
(𝑑−𝑥)
𝑏2+(𝑑−𝑥)2
𝑥
𝑎2+𝑥2
=
(𝑑−𝑥)
𝑏2+(𝑑−𝑥)2
See from finger the equation
become
sin𝜃1= sin𝜃2
i = r
So it is proved

7. Law of refraction:
x
d-x
𝜃1
𝜃2
p
A
B
a
b
d
Nsin𝜃1=
𝑎
𝑎2+𝑥2
sin𝜃2=
𝑑−𝑥
𝑏2+(𝑑−𝑥)2
Ttotal=tAP+tPB
𝑑𝑡
𝑑𝑥
=0
0=
2𝑥
2𝑣1 𝑎2+𝑥2
+
2(𝑑−𝑥)(−1)
2𝑣2 𝑏2+(𝑑−𝑥)2
0=
𝑥
𝑣1 𝑎2+𝑥2
-
(𝑑−𝑥)
𝑣2 𝑏2+(𝑑−𝑥)2
𝑥
𝑣1 𝑎2+𝑥2
=
(𝑑−𝑥)
𝑣2 𝑏2+(𝑑−𝑥)2
See from finger the equation
become
sin𝜃1 𝑣1= sin𝜃2 𝑣2
So it is proved
t=
𝑠
𝑣
t=
𝐴𝑃
𝑣1
+
𝑃𝐵
𝑣2
t=
𝑎2+𝑥2
𝑣1
+
𝑏2+(𝑑−𝑥)2
𝑣2
𝑑𝑡
𝑑𝑥
=
2𝑥
2𝑣1 𝑎2+𝑥2
+
2(𝑑−𝑥)(−1)
2𝑣2 𝑏2+(𝑑−𝑥)2
sin 𝜃1
sin 𝜃2
=
𝑣1
𝑣2
sin 𝜃1
sin 𝜃2
=n
sin𝜃1=
𝑝𝑒𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑜𝑢𝑠

8. Reflection through spherical mirror :
Spherical mirror:
A mirror whose polished reflecting surface is a part of hollow sphere is called
spherical mirror
There are two types of
spherical mirrors:
 Concave mirror
 Convex mirror
Concave mirror:
A spherical mirror whose inner side is reflecting is called concave mirror
 Size of image depend upon the
position of object.
 Both real and virtual image form by
concave mirror.
 Focus form in the front of mirror f
c

9. Convex mirror:
A spherical mirror whose outer side is reflecting is called convex mirror
 Size of image of object always smaller
then object.
 Only virtual image are formed
 Focus lie behind the mirror
f
c