# Numerical Problems Based on Polarisation of Light

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

HINT :            µ =sin ip

Sin r sin ip

R=sin -1 [sin 570 /1.57] =330.

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

Hint:                           µ =tan ip

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 ip =1.732 ,ip +r =900

Ip =tan -1  (1.732) =60 0

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 µo = 1.5442; µE = 1.5533 and λ. = 5 x 10 -5 cm.

HINT :            T =λ /2(µEO) => 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

HINT :                        I =I 0 cos 2 θ

For ordinary light                    For extra-ordinary light

I O =A2 sin 2 θ =a2 /4               I E =a2 cos 2 θ =3a2 /4

Hence  ,           I o /I E =a2/4/3a2 /4 1/3

IE = 3 IO

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.

Hint:               [S]tλ 10θ /I .C =10 x 13.2/20 x 0.1 = 660

Problem 7. Calculate the thickness of mica sheet required for making a quarter wave  plate for  A. = 5460  λ0  The indices of refraction for the ordinary and extraordinary rays in  mica are 1.586 and 1.592.

Hint:               t =λ/4 (µEo)

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

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 ,µo = 1.53 and µE = 1 .54)

Hint: t = λ/4(µEO) = 5.890 x 10-5 /4(1.54 -1.53)  = 1 .47 x 10 -3 cm.

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 = 19.80

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/cm3. Given that specific rotation of sugar solution is 60° per decimeter per unit concentration.

Hint:                           [S]Tλ= 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 µo = 1.54 and ratio of velocity extraordinary to ordinary wave is 1.006.

Hint:               t = λ /4(µEO)  =5000  x 10 -10/4(1.54 -1.53)

T=1.25 x 10 -5 cm