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MHT-CET : Physics Entrance Exam

MHT - CET : Physics - Wave Theory of Light Page 2

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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
A1A, B1C: Incident rays
AB: Incident wave front
CD: Reflected wave front
AD1, CC1: Reflected rays
MAM' and NCN' are normals to the surface at A and C
A1AM = i = Angle of incidence
MAD = r = Angle of reflection

 

Steps in the Construction of Reflected Wave Front:

 

1. Draw rays A1A, B1C parallel to each other incident on surface PQ.
2. Construct normal AB to B1C.
3. With A as centre and radius = AD, draw a semicircle.
4. Draw CD tangent to semicircle at D.
5. Extends rays CC1 and AD1 parallel to each other
reflected rays.

 

To prove i = r

 

i)

Consider triangles ABC and ADC
AC is common
CBA = ADC = 90
BC = AD = vt

\
Triangles are congruent
BCA = DAC

ii)

But BCA = 90 - i(... BCN = i , A1AM = i
DAC = 90- r (... MAD = 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
A1A, B1C: Incident rays
AB: Incident wave front
CD: Refracted wave front
AD1, CC1: Refracted rays
PAQ:
Normal to surface MN at A
P'CQ':
Normal to surface MN at C
A1AP: angle of incidence = i
QAD: angle of refraction = r
c1 = velocity of light in medium 1
c2 = velocity of light in medium 2

 

Steps in the Construction of Refracted Wave Front:

 

1.

Draw rays A1A, B1C parallel to each other and incident on surface MN

2.

Construct normal AB to B1C.

3.

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

4.

Draw tangent CD to the semicircle at D.
Radius AD =
c2t where c2 is velocity of waves in denser medium.

5.

Wave front CD represents the refracted wave front. Extend CC1, AD1 parallel to each other refracted rays.

 

To prove Snell's law:

 

PAQ is normal to MN at A
A1AP = i = angle of incidence
QAD = r = angle of refraction
\ BAC = A1AP = i
\ Q'CC1 = ACD = r
Triangles BAC and ACD are right triangles

 

Sin = 

BC

AC

 

 Sin = 

AD

AC

 

 

 

sin i

sin r

 = 

BC/AC

AD/AC

 = 

BC

AD

 = 

c1t

c2t

 = 

c1

c2

 = 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)

 

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