**Problem 1**. A glass plate refractive index 1 .54 is used as a polariser. Find angle of polarization and angle of refraction for it.

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**HINT : **µ =sin i_{p}

_{ }

_{ }Sin r sin i_{p}/µ

R=sin ^{-1} [sin 570 /1.57] =33^{0}.

**Problem 2.** The angle of polarisation for flint glass is found to 62°24′. Calculate its refractive index.

**Hint: **µ =tan i_{p}

µ =tan 62 ^{0} 24 , =1.912

**Problem 3.** A ray of light is incident on a glass surface of refractive index 1.732 at polarizing angle. Calculate the angle of refraction of the ray.

Tan i_{p} =1.732 ,i_{p} +r =90^{0}

I_{p} =tan ^{-1} (1.732) =60 ^{0}

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**Problem 4.** A plane polarized light is incident on a piece of a cut parallel to the axis. Find the least thickness for which the 0-Rtly and E-Ray combine to form plane polarized light. Given that µ_{o} = 1.5442; µ_{E} = 1.5533 and λ. = 5 x 10 ^{-5} cm.

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**HINT : **T =λ /2(µ_{E} -µ_{O}) => t = 5 x 10 -5 /2(1.5533 -1.5442) =2.75 x 10^{ -3} cm .

**Problem 5.** If the plane of vibration of incident beam makes an angle of 30° with the optic axis, compare the intensities of ordinary and extraordinary rays

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**HINT : ** I =I _{0} cos ^{2} θ

For ordinary light For extra-ordinary light

I_{ O} =A^{2} sin^{ 2} θ =a^{2} /4 I E =a^{2} cos ^{2} θ =3a^{2} /4

Hence , I _{o} /I_{ E} =a^{2}/4/3a^{2} /4 1/3

I_{E} = 3 I_{O}

_{ }

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**Problem 6.** Determine the specific rotation of a given sample of sugar solution if the plane of polarisation is turned through 13.2°. The length of the tube containing 10% sugar solution is 20 cm.

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**Hint:** [S]^{t}_{λ} 10θ /I .C =10 x 13.2/20 x 0.1 = 66^{0}

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**Problem 7.** Calculate the thickness of mica sheet required for making a quarter wave plate for A. = 5460 λ^{0} The indices of refraction for the ordinary and extraordinary rays in mica are 1.586 and 1.592.

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**Hint: **t =λ/4 (µ_{E} -µ_{o})

= 5460 x 10^{-8}/4 (1.592 -1.586) =2.275 x 10 ^{-2} cm

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**Problem 8.** Calculate the thickness of a double refracting plate capable of producing a path difference of “A/4 between ordinary and extraordinary waves. (λ = 5890 A ,µ_{o} = 1.53 and µ_{E} = 1 .54)

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**Hint:** t = λ/4(µ_{E} -µ_{O}) = 5.890 x 10_{-5} /4(1.54 -1.53) = 1 .47 x 10 _{-3} cm.

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**Problem 9.** A tube of 20 cm long with solution of 15 gm of cane sugar in 100 cc of water is placed in the path of polarization if the specific rotation of cane sugar is 66°.

**Hint: ** [S] ^{T} _{λ} 10θ/L.C

θ =SLC/L.C = 66 x 20 x 15 /10 x 100 = 19.8^{0}

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**Problem 10.** On introducing a polarimeter tube 25 cm long and containing sugar solution of known strength, it is found that the plane of polarization is rotated through 10°. Find the strength of sugar solution in g/cm^{3}. Given that specific rotation of sugar solution is 60° per decimeter per unit concentration.

**Hint:** [S]^{T}_{λ}= 10θ/ L.C = 60°

C =10θ /L.C =10 x 10 / 25 x 60 =1/15 = 0.0679 g/m3.

**Problem 11.** Calculate thickness of quarter wave plate for light of wavelength 5000 λ. Given µ_{o} = 1.54 and ratio of velocity extraordinary to ordinary wave is 1.006.

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**Hint: **t = λ /4(µ_{E} -µ_{O}) =5000 x 10 ^{-10}/4(1.54 -1.53)

T=1.25 x 10 ^{-5} cm