Worksheet: Polarization of Electromagnetic Radiation

In this worksheet, we will practice calculating the change in the intensity of light that is passed through a system of polarizing filters.

Q1:

If a polarizing filter reduces the intensity of polarized light to 5 0 . 0 % of its original value, what is the ratio of the amplitude of the electric and magnetic fields in the light incident from and emergent from the filter?


  • A 1 0 . 5 0 0
  • B 1 0 . 6 6 7
  • C 1 0 . 3 5 4
  • D 1 0 . 7 0 7
  • E 1 0 . 2 5 0

Q2:

The angle between the axes of two polarizing filters is 4 5 . 0 . By how much does the second filter reduce the intensity of the light coming through the first?

Q3:

Two polarizing sheets are placed together to form a combination with transmission axes of the polarizers oriented at an angle 𝜃 to each other. With the polarizers so aligned, the amount of light that passes through the sheets is 2 5 . 0 % of the maximum possible intensity of plane polarized light that the combination can transmit. What percentage of unpolarized light would be transmitted through the combination?

Q4:

What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1.00 kW/m2 to reduce the intensity to 10.0 W/m2 ?

Q5:

The light incident on polarizing sheet 𝑃 1 is linearly polarized at an angle of 3 0 . 0 with respect to the transmission axis of 𝑃 1 . Sheet 𝑃 2 is placed so that its axis is parallel to the polarization axis of the incident light.

What fraction of the incident light passes through 𝑃 1 ?

What fraction of the incident light is passed by the combination?

𝑃 2 is rotated so as to produce a maximum value of intensity transmitted by the combination. What is the ratio of the maximum transmitted intensity to the transmitted intensity before 𝑃 2 was rotated?

Q6:

A student places sheets 𝑃 1 and 𝑃 2 so that their transmission axes are at 4 5 . 0 and 9 0 . 0 , respectively. These angles are relative to the axis of polarization of a beam of linearly polarized light. This rotates the beam’s polarization by 9 0 . 0 .

What fraction of light passes through 𝑃 1 ?

What fraction of light passes through both sheets?

The transmission angle for 𝑃 1 is changed to 3 0 . 0 relative to the beam’s polarization axis. After the angle change, what fraction of light passes through both sheets?

Q7:

At what angle is light inside crown glass (refractive index 1.52) completely polarized when reflected from water (refractive index 1.333), as in a fish tank?

Q8:

At what angle will light reflected from diamond into air be completely polarized? Use a value of 2.419 for the refractive index of diamond.

Q9:

A scuba diver sees light reflected from the surface of water (refractive index of 1.33) above which is air (refractive index of 1.00). At what angle will this light be completely polarized?

Q10:

Light reflected at an angle of 6 2 . 5 from a gemstone in a ring into air is completely polarized.

What is the gem’s refractive index?

At what angle would the light reflected from the gem be completely polarized if the gem was underwater? Use a value of 1.33 for the refractive index of water.

Q11:

On a day when the intensity of sunlight is 1.00 kW/m2, a circular lens 0.2000 m in diameter focuses light onto water in a black aluminium beaker. Two polarising sheets of plastic are placed in front of the lens with their axes at an angle of 2 0 . 0 to each other. The aluminium beaker has a mass of 30.0 grams and contains 250 grams of water. Assuming the sunlight is unpolarised and the polarisers are 1 0 0 % efficient, what is the initial rate of heating of the water, assuming an 8 0 . 0 % absorption of the light by the water? Use a value of 4 1 8 0 / J k g C for the specific heat capacity of water and a value of 9 2 1 / J k g C for the specific heat capacity of aluminium.

  • A 1 . 3 5 × 1 0 / 2 C s
  • B 1 . 2 4 × 1 0 / 2 C s
  • C 1 . 4 7 × 1 0 / 2 C s
  • D 1 . 6 9 × 1 0 / 2 C s
  • E 1 . 5 8 × 1 0 / 2 C s

Q12:

Three polarizing sheets are placed parallel to each other. The transmission axis of the second sheet is oriented at 2 7 . 8 relative to the transmission axis of the first sheet, and the transmission axis of the third sheet is oriented at 3 6 . 7 relative to the transmission axis of the first sheet. What fraction of the intensity of an unpolarized light beam incident on the first sheet is transmitted by the third sheet?

Q13:

It is found that when light traveling in water is incident on the surface of a plastic block, Brewster’s angle is 5 2 . 0 . Find the refractive index of the plastic. Use a value of 1.33 for the refractive index of water.

Q14:

Light reflected at 5 8 . 2 from a window is completely polarized. What is the window’s refractive index?

Q15:

Suppose you put on two pairs of polarizing sunglasses with their transmission axes at an angle of 1 3 . 7 relative to each other. How much longer will it take sunlight to deposit a given amount of energy in your eye compared with a single pair of sunglasses? Assume the lenses are clear except for their polarizing characteristics.

Q16:

At what angle between the polarization axis of plane polarized light and the axis of a polarizing filter is the intensity of the light transmitted by the filter equal to one-fourth of the intensity of the light incident on the filter?

Q17:

Two polarizing sheets 𝑃 1 and 𝑃 2 are placed parallel to each other with their transmission axes oriented at an angle 𝜃 relative to each other. What is 𝜃 when the intensity of light transmitted through 𝑃 2 is equal to 33% of the intensity of unpolarized light incident on 𝑃 1 ?

Q18:

A ray of unpolarized light propagates in water. The light ray is incident on a plane layer of diamond, and the light ray reflected from the water-diamond interface is completely polarized. Find the angle of reflection of the polarized ray. Use a value of 1.33 for the refractive index of water, and use a value of 2.419 for the refractive index of diamond.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.