Question

Answer this question correctly

Answer 1

PART 1:

we know that when an unpolarized beam of intensity I ° passes through the polariser (P1)it's intensity reduces to half

Now the intensity becomes I° /2

When this beam passes through polariser P 2

According to malus Law it's intensity becomes

I°/2 cos² x

But in the question it is already given that no light is emmited from the Polaroid i.e intensity becomes 0

I°/2 cos² x = 0

cos²x = 0

x = 90°

PART 2:

Now a polariser is placed after P1 such that polarizing Axis of P2 makes an angle x with P1

we know that the intensity of light after passing through P1 is I°/2

So it's intensity after passing through P2 becomes

I°/2 cos² x

Now when this beam passes through P3 it's intensity becomes

I° /2 cos ² x cos ² x

We know from the first part that the angle between P1 and P3 is 90

and the angle between P1 and P2 is x

So the angle between P1 and P3 will become

90 - x

I° /2 cos ² x cos ² (90-x)

I° /2 cos ² x sin ² x..(1)

we know that

sin 2x =2 sin x .cos x

squaring both the sides,

sin ²2x =2² sin² x .cos² x

sin² x .cos² x = sin²2x/4...(2)

Substituting 2 in 1

I° /2 sin² 2x /4

I° /8 sin²(2x)

Answer 2

Answer:

Option(A)

Explanation:

Let Initial Intensity = I₀

So, Intensity of light after transmission from first polaroid = I₀/2

Intensity of light emitted from P₃

I₁ = I₀/2 cos²θ

Intensity of light transmitted from last Polaroid :

P₂ = I₁cos²(90 - θ)

=> P₂ = I₀/2[cos²θsin²θ]

=> P₂ = I₀/8[2 sinθ cosθ)²

=> P₂ = (I₀/8) sin² 2θ

Hope it helps!