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Question : 26
Total: 27
(a) Describe any two characteristic features which distinguish interference and diffraction phenomena. Derive the expression for the intensity at a point of the interference pattern in Young's double slit experiment.
(b) In the diffraction due to a single slit experiment, the aperture of the slit is 3mm 620 nm 1.5 m
OR
(a) Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.
(b) Three lenses of focal lengths+ 10 cm , − 10 cm + 30 cm
(b) In the diffraction due to a single slit experiment, the aperture of the slit is 3
OR
(a) Under what conditions is the phenomenon of total internal reflection of light observed? Obtain the relation between the critical angle of incidence and the refractive index of the medium.
(b) Three lenses of focal lengths
Solution:
(a) Two characteristic features of distinction
Derivation of the expression for the intensity
(b) Calculation of separation between the first order
(a) (Any two of the following)
(i) Interference pattern has number of equally spaced bright and dark bands while diffraction pattern has central bright maximum which is twice as wide as the other maxima.
(ii) Interference is obtained by the superposing two waves originating from two narrow slits. The diffraction pattern is the superposition of the continuous family of waves originating from each point on a single slit.
(iii) In interference pattern, the intensity of all bright fringes is same, while in diffraction pattern intensity of bright fringes go on decreasing with the increasing order of the maxima.
(iv) In interference pattern, the first maximum falls at an angle of
a a
Displacement produced by sourceS 1
Y 1 = a cos ω t
Displacement produced by the other source 'S 2 ′
γ 2 = a cos ( ω t + ϕ )
Resultant displacementY = Y 1 + Y 2
= a [ cos ω t + cos ( ω t + ϕ )
= 2 a cos (
) cos ( ω t +
)
Amplitude of resultant wave
A = 2 a cos (
)
IntensityI ∝ A 2
I = K A 2 = K 4 a 2 cos 2 (
)
(b) Distance of first order minima from centre of the central maxima= X D 1 =
Distance of third order maxima from centre of the central maximaX B 3 =
∴ = X B 3 − X D 1
=
−
=
=
= 775 × 10 − 6 m
= 7.75 × 10 − 4 m
OR
(a) Two conditions of total internal reflection
(b) Obtaining the relation
(c) Calculating of the position of the final image
(a) (i) Light travels from denser to rarer medium.
(ii) Angle of incidence is more than the critical angle
(b) For the Grazing incidence
µ s i n i C = s i n 90 ∘
µ =
(c) For convex lens of focal length10 cm
=
−
=
−
⇒ v 1 = 15 cm
Object distance for concave lens
u 2 = 15 − 5 = 10 cm
=
−
=
−
v 2 = ∞
For third lens
=
−
=
−
v 3 = 30 cm
Derivation of the expression for the intensity
(b) Calculation of separation between the first order
(a) (Any two of the following)
(i) Interference pattern has number of equally spaced bright and dark bands while diffraction pattern has central bright maximum which is twice as wide as the other maxima.
(ii) Interference is obtained by the superposing two waves originating from two narrow slits. The diffraction pattern is the superposition of the continuous family of waves originating from each point on a single slit.
(iii) In interference pattern, the intensity of all bright fringes is same, while in diffraction pattern intensity of bright fringes go on decreasing with the increasing order of the maxima.
(iv) In interference pattern, the first maximum falls at an angle of
Displacement produced by source
Displacement produced by the other source '
Resultant displacement
Amplitude of resultant wave
Intensity
(b) Distance of first order minima from centre of the central maxima
Distance of third order maxima from centre of the central maxima
OR
(a) Two conditions of total internal reflection
(b) Obtaining the relation
(c) Calculating of the position of the final image
(a) (i) Light travels from denser to rarer medium.
(ii) Angle of incidence is more than the critical angle
(b) For the Grazing incidence
(c) For convex lens of focal length
Object distance for concave lens
For third lens
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