Three polaroid sheets are co-axially placed such that pass axis of polaroids 2 and 3 make 3 0 ∘ and 9 0 ∘ with pass axis of sheet. If I 0 is the intensity of unpolarised light entering first sheet,

Question

Three polaroid sheets are co-axially placed such that pass axis of polaroids 2 and 3 make 3 0 ∘ and 9 0 ∘ with pass axis of sheet. If I 0 ​ is the intensity of unpolarised light entering first sheet, the intensity of the emergent light through 3 r d sheet is

TestHub · Accepted Answer

Intensity of unpolarised light entering the first polaroid is $I_{0}$ .

Intensity of light emerging from the first polaroid is $I_{1} = \frac{I _{0}}{2}$ .

The angle between the pass axis of the first and second polaroid is $θ_{1} = 3 0^{\circ}$ .

Using Malus's law, the intensity of light emerging from the second polaroid is:

$I_{2} = I_{1} cos^{2} (3 0^{\circ}) = \frac{I _{0}}{2} \times (\frac{3}{2})^{2} = \frac{I _{0}}{2} \times \frac{3}{4} = \frac{3 I _{0}}{8}$

The angle between the pass axis of the first and third polaroid is $9 0^{\circ}$ . Therefore, the angle between the pass axis of the second and third polaroid is $θ_{2} = 9 0^{\circ} - 3 0^{\circ} = 6 0^{\circ}$ .

The intensity of light emerging from the third polaroid is:

$I_{3} = I_{2} cos^{2} (6 0^{\circ}) = \frac{3 I _{0}}{8} \times (\frac{1}{2})^{2} = \frac{3 I _{0}}{8} \times \frac{1}{4} = \frac{3 I _{0}}{32}$

Answer: $\frac{3 I _{0}}{32}$

Physics - Wave Optics Question with Solution | TestHub

Options:

Doubts & Discussion