4.

Reflection
of Light


Laws of
Reflection of Light:
1. The angle of incidence is equal to the angle of reflection.
2. The incident ray, reflected ray and the normal lie in the same plane.
3. The incident ray and the reflected ray lie on opposite sides of the
normal.


Derivation (According to Huygen's Theory)


PQ: Plane reflecting surface
A_{1}A, B_{1}C: Incident rays
AB: Incident wave front
CD: Reflected wave front
AD_{1}, CC_{1}: Reflected rays
MAM' and NCN' are normals to the surface at A and C
ÐA_{1}AM
= i = Angle of
incidence
ÐMAD = r = Angle of
reflection




Steps in the Construction of Reflected Wave Front:


1. Draw rays A_{1}A, B_{1}C parallel to each
other incident on surface PQ.
2. Construct normal AB to B_{1}C.
3. With A as centre and radius = AD, draw a semicircle.
4. Draw CD tangent to semicircle at D.
5. Extends rays CC_{1} and AD_{1} parallel to each other ® reflected rays.


To prove i = r


i)

Consider triangles ABC and ADC
AC is common
ÐCBA = ÐADC = 90°
BC = AD = vt
\
Triangles are congruent
ÐBCA = ÐDAC

ii)

But ÐBCA = 90°  i(^{.}.^{.} ÐBCN = i , ÐA1AM = i
ÐDAC = 90° r (^{.}.^{.} ÐMAD = r )
\
90°  i = 90°  r
\ i = r






5.

Refraction
of Light


Laws of Refraction of Light:


1.

The refractive index (n) of a pair of media is a constant
n =

sin i


sin r


= constant

where i: angle of incidence
r: angle of refraction

2.

The incident ray, refracted ray and the normal lie in the
same plane.

3.

The incident ray and the refracted ray lie on opposite
sides of the normal.



Derivation (According to Huygen's Theory)




MN: Refracting surface
A_{1}A, B_{1}C: Incident rays
AB: Incident wave front
CD: Refracted wave front
AD_{1}, CC_{1}: Refracted rays
PAQ: Normal to surface MN
at A
P'CQ': Normal to surface MN
at C
ÐA_{1}AP:
angle of incidence = i
ÐQAD: angle of
refraction = r
c_{1} = velocity of
light in medium 1
c_{2} = velocity of
light in medium 2


Steps in the Construction of Refracted Wave Front:


1.

Draw rays A_{1}A, B_{1}C parallel to each
other and incident on surface MN

2.

Construct normal AB to B_{1}C.

3.

With A as centre and a radius R = AD ,
construct a semicircle.

4.

Draw tangent CD to the semicircle at D.
Radius AD = c_{2}t where c_{2} is velocity
of waves in denser medium.

5.

Wave front CD represents the refracted wave front. Extend
CC_{1}, AD_{1} parallel to each other ® refracted
rays.



To prove Snell's law:


PAQ is normal to MN at A
ÐA_{1}AP
= i = angle of
incidence
ÐQAD = r = angle of
refraction
\ ÐBAC = ÐA_{1}AP
= i
\ ÐQ'CC_{1}
= ÐACD = r
Triangles BAC and ACD are right triangles


Sin i =

BC


AC





Sin r =

AD


AC







sin i


sin r


=

BC/AC


AD/AC


=

BC


AD


=

c_{1}t


c_{2}t


=

c_{1}


c_{2}


= constant (n)





The constant (n) is called the refractive index of
medium 1 w.r. to medium 2.





n =

sin i


sin r


= constant (Snell's law)

