AMU Engineering 2018 solved paper Solved Paper

In Young's double slit experiment, intensity at any point on the screen is given by
I=I1+I2+2√I1I2‌cos‌ϕ ........(i)
where, I1 and I2 are intensity of two sources.
But both sources are identical, hence
I1=I2=I0‌‌‌[∴ from Eq. (i)]
I=I0+I0+2√I0I0‌cos‌ϕ
I=2I0+2I0‌cos‌ϕ
=2I0(1+cos‌ϕ)=2I0.2cos2

ϕ

2

I=4I0cos2

ϕ/

2

.......(ii)
When path difference is λ, then phase difference ϕ=2π
∴ From Eq. (ii),
I=4I0cos2

2π

2

I=4I0=k(given ) .........(iii)
Again when path difference is

λ

3

, then phase difference ϕ=

2π

λ

.

λ

3

=

2π

3

∴ From Eq. (ii), I=4I0cos2(

2π∕3

2

)=4I0cos2

π

3

=4I0.

1

4

=k.

1

4

=

k

4