Two Nicol prisms are first crossed and then one of them is rotated through 60°. The percentage of incident light transmitted is

Question

Two Nicol prisms are first crossed and then one of them is rotated through 60°. The percentage of incident light transmitted is (A) 1.25 (B) 25.0 (C) 37.5 (D) 50

Tardigrade Admin · Accepted Answer

If, I0 is intensity of unpolarized light, then from 1 st Nicol prism, I1=(I0/2) From 2 nd Nicol prism, I2=I1 cos 2(90°-60°) =(I0/2)((√3/2))2=(3/8) I0 ⇒ (I2/I0)=37.5

Q. Two Nicol prisms are first crossed and then one of them is rotated through $6 0^{\circ}$ . The percentage of incident light transmitted is

1.25

25.0

37.5

50

If, $I_{0}$ is intensity of unpolarized light,
then from 1 st Nicol prism, $I_{1} = \frac{I _{0}}{2}$
From 2 nd Nicol prism, $I_{2} = I_{1} cos^{2} (9 0^{\circ} - 6 0^{\circ})$
$= \frac{I _{0}}{2} (\frac{3}{2})^{2} = \frac{3}{8} I_{0}$
$\Rightarrow \frac{I _{2}}{I _{0}} = 37.5$

Q. Two Nicol prisms are first crossed and then one of them is rotated through 60∘. The percentage of incident light transmitted is

1.25

25.0

37.5

50

If, I0​ is intensity of unpolarized light, then from 1 st Nicol prism, I1​=2I0​​ From 2 nd Nicol prism, I2​=I1​cos2(90∘−60∘) =2I0​​(23​​)2=83​I0​ ⇒I0​I2​​=37.5

Q. Two Nicol prisms are first crossed and then one of them is rotated through $6 0^{\circ}$ . The percentage of incident light transmitted is

If, $I_{0}$ is intensity of unpolarized light,
then from 1 st Nicol prism, $I_{1} = \frac{I _{0}}{2}$
From 2 nd Nicol prism, $I_{2} = I_{1} cos^{2} (9 0^{\circ} - 6 0^{\circ})$
$= \frac{I _{0}}{2} (\frac{3}{2})^{2} = \frac{3}{8} I_{0}$
$\Rightarrow \frac{I _{2}}{I _{0}} = 37.5$