(a) (i) Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism. What is the angle of prism? (cos 41^o = 0.75)
(ii) A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to ¾ of the angle of the prism. What is the angle of deviation?

(b) A thin prism of angle 6o made of glass of refractive index 1.5 is combined with another prism made of glass of m = 1.6 to produce dispersion without deviation. What is the angle of second prism?

OR
(a) (i) In the Young’s double slit experiment using a monochromatic light of wavelength O, what is the path difference (in terms of an integer n) corresponding to any point having half the peak intensity?
(ii) Light of wavelength 6.5 × 10^–7 m is made incident on two slits 1 mm apart. What will be the distance between third dark fringe and fifth bright fringe on a screen distant 1 m from the slits?

(b) (i) A beam of unpolarised light passes through a tourmaline crystal A and then through another such crystal B oriented so that the principal plane is parallel to A. The intensity of emergent light is I₀. Now B is rotated by 45º about the ray. What will be the intensity of emergent light?
(ii) If the polarizing angle of a piece of glass for green light is 54.74°, then the angle of minimum deviation for an equilateral prism made of same glass is
[Given, tan 54.74° = 1.414]

Question

(a) (i) Angle of minimum deviation for a prism of refractive index 1.5 is equal to the angle of prism. What is the angle of prism? (cos 41^o = 0.75)
(ii) A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to ¾ of the angle of the prism. What is the angle of deviation?

(b) A thin prism of angle 6o made of glass of refractive index 1.5 is combined with another prism made of glass of m = 1.6 to produce dispersion without deviation. What is the angle of second prism?

OR
(a) (i) In the Young’s double slit experiment using a monochromatic light of wavelength O, what is the path difference (in terms of an integer n) corresponding to any point having half the peak intensity?
(ii) Light of wavelength 6.5 × 10^–7 m is made incident on two slits 1 mm apart. What will be the distance between third dark fringe and fifth bright fringe on a screen distant 1 m from the slits?

(b) (i) A beam of unpolarised light passes through a tourmaline crystal A and then through another such crystal B oriented so that the principal plane is parallel to A. The intensity of emergent light is I₀. Now B is rotated by 45º about the ray. What will be the intensity of emergent light?
(ii) If the polarizing angle of a piece of glass for green light is 54.74°, then the angle of minimum deviation for an equilateral prism made of same glass is
[Given, tan 54.74° = 1.414]

Accepted Answer

(a) (i) μ=sin isin A22=sin 45sin A2⇒sin⁡A2=122=12A2=30∘⇒A=60∘(ii)Given δm=Athen by using μ=sin A+δm2sin A2μ=sin A+A2sin A2=sin Asin A2=2cos A2sin A=2sin A2cos A2 1.5=2cos A2⇒0.75=cos A2 41∘=A2⇒A=82∘(b)   (μ-1)A=μ'-1A' A'=(μ-1)Aμ'-1=(1.5-1)6∘(1.6-1)=5∘OR (a) (i) The intensity I is given asI=I0cos2 ϕ2  where I0 is the peak intensity Here I=Io2, ∴Io2=Iocos2⁡ϕ2 ∴ϕ=π2(2n+1)For a phase difference of 2p the path difference is lFor a phase difference of(2n+1)π2 , the path difference is (2n+1)λ4(ii)  x5=nλDd=5×6.5×10-7×110-3=32.5×10-4 m x3=(2n-1)12Dλd=5×6.5×10-7×12×10-3  =16.25×10-4 m x5-x3=16.25×10-4 m=1.625 mm.(b) (i) According to law of Malus,I=I0cos2⁡θ=I0cos⁡45∘2=I0122=I02(ii)By principle of polarization,  μ=tan θpor μ=tan 54.74∘ or μ=1.414For an equilateral prism  ∠A=60∘∴μ=sin⁡A+δ2sin⁡(A/2)=sin⁡60∘+δ2sin⁡60∘/2  or, 1.141×12=sin⁡60∘+δ2[∵1.414=2]  or, 22=sin⁡60∘+δ2 or 12=sin⁡60∘+δ2  or, sin⁡45∘=sin⁡60∘+δ2 or 45∘=60∘+δ2

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