JEE Main 27-Jan-2024 Shift 2 Solved Paper

Let I0 be intensity of unpolarised light incident on first polaroid.
I1= Intensity of light transmitted from 1‌st ‌ polaroid
=‌

I0

2

θ be the angle between 1‌st ‌ and 2‌nd ‌ polaroid
ϕ be the angle between 2‌nd ‌ and 3‌rd ‌ polaroid
θ+ϕ=90∘ (as 1‌st ‌ and 3‌rd ‌ polaroid are crossed)
ϕ=90∘−θ
I2= Intensity from 2‌nd ‌ polaroid
I2=I1cos2θ=‌

I0

2

cos2θ
I3= Intensity from 3‌rd ‌ polaroid
I3=I2cos2φ
I3=I1cos2θcos2ϕ
I3=‌

I0

2

cos2θcos2ϕ
ϕ=90−θ
‌I3=‌

I0

2

cos2θsin‌2θ
‌I3=‌

I0

2

[‌

2sin‌θ‌cos‌θ

2

]2
‌I3=‌

I0

8

sin‌22θ
I3 will be maximum when sin‌2θ=1
‌2θ=90∘
‌θ=45∘