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Conceptual questions

Under what circumstances is the phase of light changed by reflection? Is the phase related to polarization?

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Can a sound wave in air be polarized? Explain.

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No light passes through two perfect polarizing filters with perpendicular axes. However, if a third polarizing filter is placed between the original two, some light can pass. Why is this? Under what circumstances does most of the light pass?

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Explain what happens to the energy carried by light that it is dimmed by passing it through two crossed polarizing filters.

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When particles scattering light are much smaller than its wavelength, the amount of scattering is proportional to 1 / λ 4 size 12{1/λ rSup { size 8{4} } } {} . Does this mean there is more scattering for small λ size 12{λ} {} than large λ size 12{λ} {} ? How does this relate to the fact that the sky is blue?

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Using the information given in the preceding question, explain why sunsets are red.

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When light is reflected at Brewster’s angle from a smooth surface, it is 100% size 12{"100"%} {} polarized parallel to the surface. Part of the light will be refracted into the surface. Describe how you would do an experiment to determine the polarization of the refracted light. What direction would you expect the polarization to have and would you expect it to be 100% size 12{"100"%} {} ?

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Problems&Exercises

What angle is needed between the direction of polarized light and the axis of a polarizing filter to cut its intensity in half?

45 . size 12{"45" "." 0°} {}

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The angle between the axes of two polarizing filters is 45 . size 12{"45" "." 0°} {} . By how much does the second filter reduce the intensity of the light coming through the first?

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If you have completely polarized light of intensity 150 W / m 2 size 12{"150"`W/m rSup { size 8{2} } } {} , what will its intensity be after passing through a polarizing filter with its axis at an 89 . size 12{"89" "." 0°} {} angle to the light’s polarization direction?

45 . 7 mW/m 2 size 12{"45" "." 7`"mW/m" rSup { size 8{2} } } {}

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What angle would the axis of a polarizing filter need to make with the direction of polarized light of intensity 1 . 00 kW/m 2 size 12{1 "." "00"`"kW/m" rSup { size 8{2} } } {} to reduce the intensity to 10 . 0 W/m 2 size 12{10 "." 0`"W/m" rSup { size 8{2} } } {} ?

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At the end of [link] , it was stated that the intensity of polarized light is reduced to 90 . 0% size 12{"90" "." 0%} {} of its original value by passing through a polarizing filter with its axis at an angle of 18 . size 12{"18" "." 4°} {} to the direction of polarization. Verify this statement.

90 . 0% size 12{"90" "." 0%} {}

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Show that if you have three polarizing filters, with the second at an angle of 45º size 12{"45"°} {} to the first and the third at an angle of 90 . size 12{"90" "." 0°} {} to the first, the intensity of light passed by the first will be reduced to 25 . 0% size 12{"25" "." 0%} {} of its value. (This is in contrast to having only the first and third, which reduces the intensity to zero, so that placing the second between them increases the intensity of the transmitted light.)

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Prove that, if I is the intensity of light transmitted by two polarizing filters with axes at an angle θ and I is the intensity when the axes are at an angle 90.0º θ, then I + I = I 0, the original intensity. (Hint: Use the trigonometric identities cos ( 90.0º θ ) = sin θ and cos 2 θ + sin 2 θ = 1. )

I 0 size 12{I rSub { size 8{0} } } {}

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At what angle will light reflected from diamond be completely polarized?

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What is Brewster’s angle for light traveling in water that is reflected from crown glass?

48 . size 12{"48" "." 8°} {}

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A scuba diver sees light reflected from the water’s surface. At what angle will this light be completely polarized?

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At what angle is light inside crown glass completely polarized when reflected from water, as in a fish tank?

41 . size 12{"41" "." 2°} {}

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Light reflected at 55 . size 12{"55" "." 6°} {} from a window is completely polarized. What is the window’s index of refraction and the likely substance of which it is made?

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(a) Light reflected at 62 . size 12{"62" "." 5°} {} from a gemstone in a ring is completely polarized. Can the gem be a diamond? (b) At what angle would the light be completely polarized if the gem was in water?

(a) 1.92, not diamond (Zircon)

(b) 55 . size 12{"55" "." 2°} {}

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If θ b is Brewster’s angle for light reflected from the top of an interface between two substances, and θ b is Brewster’s angle for light reflected from below, prove that θ b + θ b = 90 . 0º. size 12{θ rSub { size 8{b} } + { {θ}} sup { ' } rSub { size 8{b} } ="90" "." 0°} {}

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Integrated Concepts

If a polarizing filter reduces the intensity of polarized light to 50 . 0% size 12{"50" "." 0%} {} of its original value, by how much are the electric and magnetic fields reduced?

B 2 = 0 . 707 B 1 size 12{B rSub { size 8{2} } =0 "." "707"B rSub { size 8{1} } } {}

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Integrated Concepts

Suppose you put on two pairs of Polaroid sunglasses with their axes at an angle of 15 . size 12{"15" "." 0°} {} . How much longer will it take the light 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.

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Integrated Concepts

(a) On a day when the intensity of sunlight is 1 . 00 kW / m 2 size 12{1 "." "00"`"kW"/m rSup { size 8{2} } } {} , a circular lens 0.200 m in diameter focuses light onto water in a black beaker. Two polarizing sheets of plastic are placed in front of the lens with their axes at an angle of 20 . 0º. size 12{"20" "." 0°} {} Assuming the sunlight is unpolarized and the polarizers are 100% size 12{"100"%} {} efficient, what is the initial rate of heating of the water in ºC / s size 12{°C/s} {} , assuming it is 80 . 0% size 12{"80" "." 0%} {} absorbed? The aluminum beaker has a mass of 30.0 grams and contains 250 grams of water. (b) Do the polarizing filters get hot? Explain.

(a) 2.07 × 10 -2 °C/s

(b) Yes, the polarizing filters get hot because they absorb some of the lost energy from the sunlight.

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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