Polaroids at an Angle

Q. Two polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle ${45}^o$ with that of $P_1$. The intensity of transmitted light through $P_2$ is

1. $\frac{I_0}{16}$
2. $\frac{I_0}{8}$
3. $\frac{I_0}{2}$
4. $\frac{I_0}{4}$

Q. Two polaroids are crossed to each other. When one of them is rotated through ${60}^{\circ }$, then what percentage of the incident unpolarised light will be transmitted by the polaroids?

1. $37.5\%$
2. $100\%$
3. $50\%$
4. $66.5\%$

Q.

A polaroid is placed at 45° to an incoming light of intensity I_o. Now the intensity of light passing through the poloroid after polarisation would be:

1. 

2. 

3. 

4. Zero

Q. Two beams $A$ and $B$ of plane polarized light with mutually perpendicular planes of polarization are through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through ${30}^{\circ }$ makes the two beams appear equally bright. If the initial intensities is of the two beams are $I_A$ and $I_B$ respectively, then $\frac{I_A}{I_B}$ is equal to,

1. $3$
2. $1$
3. $\frac{3}{2}$
4. $\frac{1}{3}$

Q. When unpolarized beam of light of intensity I° is incident on two polarizer in contact If the angle between the axes of two polarizer is 60^° then the intensity of light inally emerging from the combination i

Q.

A beam of unpolarised light passes through a tourmaline crystal A and then it passes through a tourmaline crystal B oriented so that its principal plane is parallel to that of A. the intensity of emergent light is $I_0$. Now B is rotated by ${45}^{\circ }$ about the ray. The emergent light will have intensity:

1. $\frac{2}{I_0}$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{\sqrt{2}}$
4. $\frac{\sqrt{2}}{I_0}$

Q. Plane polarized light is incident on an analyser. The intensity then becomes three fourth. The angle of the axis of the analyser with the polarization axis of beam is:

1. Zero
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q.

A polaroid is placed at 45^o to an incoming light of intensity I₀. Now the intensity of light passing through polaroid after polarisation would be

1. I₀

2. I₀ / 2

3. I₀ / 4

4. Zero

Q.

The intensity of light pulse travelling in an optical fiber decrease according to the relation $I=I_0{e}^{-\alpha x}$. The intensity of light is reduced to $20\%$of its initial value after a distance x equal to

1. $\log \left(\frac{1}{\alpha }\right)$

2. $\log \left(\alpha \right)$

3. $\frac{\left(\log \left(5\right)\right)}{\alpha }$

4. $\log \left(\frac{5}{\alpha }\right)$

Q. Two polaroids $P_1\text{and}{P}_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1.$ A third polaroid $P_3$ is kept in between $P_1\text{and}{P}_2$ such that its axis makes an angle ${45}^{\circ }$ with that of $P_1.$ The intensity of transmitted light through $P_2$ is

1. $\frac{I_0}{2}$
2. $\frac{I_0}{4}$
3. $\frac{I_0}{8}$
4. $\frac{I_0}{16}$

Q. Two polaroids are crossed to each other. Now, one of them is rotated through ${60}^{\circ }.$ What percentage of incident unpolarized light will pass through the system?

Q. Unpolarized light of intensity $32W{m}^{-2}$ passes through three polarisers such that the transmission axis of the last polarizer is perpendicular to that of the first. The intensity of final emerging light is $3W{m}^{-2}$. The angle between the transmission axes of the first two polarizers will

1. ${10}^{\circ }$
2. ${30}^{\circ }$
3. ${45}^{\circ }$
4. ${60}^{\circ }$

Q. Unpolarised light of intensity $32W{m}^{-2}$ passes through three polarisers such that the transmission axis of the last polarizer is perpendicular to that of the first. At what angle will the transmitted intensity be maximum?

1. ${60}^{\circ }$
2. ${15}^{\circ }$
3. ${30}^{\circ }$
4. ${45}^{\circ }$

Q. A water film $(\mu =1.33)$ is illuminated normally by a light $\lambda =6.65nm$. In order that the film appears bright, the minimum thickness of the film is:

1. 3.325 nm
2. 1.16 nm
3. 2.5 nm
4. 1.25 nm

Q. A system of three polarizers $P_1,P_2,P_3$ is set up such that the pass axis of $P_3$, is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at ${60}^{\circ }$ to the pass axis of $P_3$. When a beam of unpolarized light, of intensity $I_0$, is incident on $P_1$, the intensity of light transmitted by the three polarizers is $I$. The ratio $\left(\frac{I_0}{I}\right)$ equals (nearly) :

1. $5.33$
2. $16.00$
3. $1.80$
4. $10.67$

Q. In Fig., shown $AB$ is the principal axis of the concave mirror. A point object moves on the line $PQ$ which makes small angle ${}^{\prime }{\theta }^{\prime }$ with the principal axis. Show that image also moves in straight line making same angle $\theta$ with principle axis.

Q. Does the principle of conservation of energy hold for interference and diffraction phenomena? Explain briefly.

Q. Two polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle ${45}^o$ with that of $P_1$. The intensity of transmitted light through $P_2$ is

1. $\frac{I_0}{16}$
2. $\frac{I_0}{2}$
3. $\frac{I_0}{4}$
4. $\frac{I_0}{8}$

Q. If the angle between incident beam and crystallographic plane is ${30}^{\circ }$, then the scattering angle is -

1. ${125}^{\circ }$
2. ${115}^{\circ }$
3. ${110}^{\circ }$
4. ${120}^{\circ }$

Q. Plane polarized light is incident on an analyser. The intensity then becomes three fourth. The angle of the axis of the analyser with the polarization axis of beam is:

1. ${30}^{\circ }$
2. ${45}^{\circ }$
3. ${60}^{\circ }$
4. Zero

Q. The edge of an aluminium cube is $10cm$ long. One face of the cube is firmly fixed to a vertical wall. A mass of $100kg$ is then attached to the opposite face of the cube. The vertical deflection of this face is
(Shear modulus of aluminium $=25GPa,g=10{ms}^{-2}$ )

1. $4\times {10}^{-5}m$
2. $4\times {10}^{-8}m$
3. $4\times {10}^{-7}m$
4. $4\times {10}^{-6}m$

Q. Two Polaroids $P_1$ and $P_2$ are placed with their pass axes perpendicular to each other.
UnPolarised light of intensity $I_0$ is incident on $P_1$. A third Polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its pass axis makes an angle of ${30}^0$ with that of $P_1$. Determine the intensity of light transmitted through $P_1,P_2$ and $P_3$:

Q. Unpolarized light of intensity I passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be $\frac{1}{2}$. Now another identical polarizer C is placed between A and B . The intensity beyond B is now found to be $\frac{I}{8}$. What angle polarizer C makes with A?

Q. A mirror is placed at an angle of ${30}^o$ with respect to y-axis(see figure). A light rat travelling in the negative y-direction strikes the mirror. The direction of the reflected ray is given by the vector.

1. $\hat{i}$
2. $\hat{i}-2\hat{j}$
3. $\hat{i}-\sqrt{3}\hat{j}$
4. $\sqrt{3}\hat{i}-\hat{j}$

Q. Two beams $A$ and $B$ of plane polarized light with mutually perpendicular planes of polarization are through a polaroid. From the position when the beam $A$ has maximum intensity (and beam $B$ has zero intensity), a rotation of polaroid through ${30}^{\circ }$ makes the two beams appear equally bright. If the initial intensities is of the two beams are $I_A$ and $I_B$ respectively, then $\frac{I_A}{I_B}$ is equal to,

1. $3$
2. $\frac{1}{3}$
3. $1$
4. $\frac{3}{2}$

Q. 28.Unpolarised light of intensity I is incident on a polarizer and the emerging light strikes a second polarizingfilter with its axis at 45 degrees to that of the first, Determine a)The intensity of the emerging beam and b)Its state of polarization

Q.

A bar magnet of length $16cm$ has a pole strength of $500\times {10}^{-3}Am$ The angle at which it should be placed to the direction of external magnetic field of induction $2.5G$ so that it may experience a torque of $\sqrt{3}\times {10}^{-5}$ Nm is :

1. $\frac{\pi }{2}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{3}$
4. $\pi$

Q. A ray of light enters a spherical drop of water of refractive index $\mu$ as shown in fig. Select the correct statement(s).

1. Incident rays are partially reflected at point A
2. Incident rays are totally reflected at point A
3. Incident rays are totally transmitted through A
4. None of these

Q. Two polarizer are oriented with transmission planes making an angle of 60 the percentage of incident unpolarized light that passes the system iz

Q. A light of intensity 10 passes through a material of thickness d, then the intensity will be.

1. $l=l_0{e}^{-d\lambda }$
2. $l=l_0{e}^{d\lambda }$
3. $l=l_0(l-e^{-d\lambda })$
4. None of these