Question

verify laws of refraction of light on the basis of wave
theory. also comment about nature of
image format ​

Answer 1

Explanation:

Let XY be the plane refracting surface.

Let μ

1

,μ

2

be the refractive indices of first and final medium.

Let AB be a plane wave front advancing obliquely toward XY.

When A reaches O,B will be at P

According to

Huygen's principle, secondary wavelets will orriginate from O.

Rays between AO and BQ will reach XY and spread over hemispheres of increasing radii

Let V

1

,V

2

be the velocities in media 1 and 2.

The distance covered ON will be covered in the same times when the distance. PQ is covered in medium 1.

V

1

ON

=

V

1

PQ

= time taken .....(1)

Now, in ΔOPQ,tani=

PO

PQ

=

AB

PQ

.PQ=ABtani and

OP=OQcosi

In ΔONQ,sinr=

OQ

ON

=

AB

ON

cosi,ON=

cosi

ABsinr

Equation 1 becomes.

PQ

ON

=

V

1

V

1

=

cosiABtani

ABsinr

=

sini

sinr

, Also

V

1

V

2

=

c/n

1

c/n

2

=

n

2

n

1

.

∴

sinr

sini

=

n

1

n

2

. Hence snell's law is proved.

Given that, the ratio of intensities of co-herent sources =81:1

I

2

I

1

=

I

81

⟹I

1

=81K&I

2

=K

K is constant

I

min

I

max

=?

I

max

=I

1

+I

2

+2I

1

I

2

cosϕ if cosϕ=1

I

max

=I

1

+I

2

+2I

1

I

2

I

max

=(

I

1

)

2

+(

I

2

)

2

+2

I

1

I

2

I

max

=(

I

1

+

I

2

)

2

Similarly cosϕ=−I

I

min

=I

1

+I

2

−2I

2

I

2

I

min

=(

I

1

−

I

2

)

2

Now,

I

min

I

max

,

(

I

1

−

I

2

)

2

(

I

2

+

I

2

)

2

=

(

81K

−

K

)

2

(

81K

+

K

)

2

=

(8

K

)

2

(10

K

)

2

I

min

I

max

=

64

100

I

min

I

max

=

16

25

solution