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Question : 26
Total: 26
(a) Draw a ray diagram to show image formation when the concave mirror produces a real, inverted and magnified image of the object.
(b) Obtain the mirror formula and write the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a refracting telescope.
OR
(a) Define a wavefront. Using Huygens' principle, verify the laws of reflection at a plane surface.
(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? Explain.
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle. Explain why.
(b) Obtain the mirror formula and write the expression for the linear magnification.
(c) Explain two advantages of a reflecting telescope over a refracting telescope.
OR
(a) Define a wavefront. Using Huygens' principle, verify the laws of reflection at a plane surface.
(b) In a single slit diffraction experiment, the width of the slit is made double the original width. How does this affect the size and intensity of the central diffraction band? Explain.
(c) When a tiny circular obstacle is placed in the path of light from a distant source, a bright spot is seen at the centre of the obstacle. Explain why.
Solution:
(a) Ray diagram to show the required image formation
(b) Derivation of mirror formula
Expression for linear magnification
(c) Two advantages of a reflecting telescope over a refracting telescope
(a)
(b) In the above figure,△ BAP △ B ′ A ′ P
⇒
=
Similarly,△ MNF △ B ′ A ′ F
⇒
=
As MN = BA
NF ≈ PF
FA ′ = PA ′ − PF
∴
=
Using equation (i) and (iii)
=
For the given figure, as per the sign convention,
PA = − u
PA ′ = − v
PF = − f
⇒
=
=
u v − u f = v f
Dividing each term by uvf, we get
−
=
⇒
=
+
Linear magnification= −
(c) Advantages of reflecting telescope over refracting telescope
(i) Mechanical support is easier.
(ii) Magnifying power is large.
(iii) Resolving power is large.
(iv) Spherical aberration is reduced.
(v) Free from chromatic aberration.
OR
(a) Definition of wave front Verification of laws of reflection
(b) Explanation of the effect on the size and intensity of central maxima
(c) Explanation of the bright spot in the shadow of the obstacle
(a) The wave front may be defined as a surface of constant phase.
(Alternatively: The wave front is the loci of all points that are in the same phase.)
Let the speed of the wave in the medium be 'v
Let the time taken by the wave front, to advance from pointB
C τ
HenceBC = v τ
LetC E
DistanceAE = v τ = BC
△ A E C △ A B C
B A C = ∠ E C A
⇒ ∠ i = ∠ r
(b) Size of central maxima reduces to half,
( ∴ . = 2
)
Intensity increases.
This is because the amount of light, entering the slit, has increased and the area, over which it falls, decreases.
(Also accept if the student just writes that the intensity becomes four fold.)
(c) This is because of diffraction of light.
(b) Derivation of mirror formula
Expression for linear magnification
(c) Two advantages of a reflecting telescope over a refracting telescope
(a)
(b) In the above figure,
Similarly,
Using equation (i) and (iii)
For the given figure, as per the sign convention,
Dividing each term by uvf, we get
Linear magnification
(c) Advantages of reflecting telescope over refracting telescope
(i) Mechanical support is easier.
(ii) Magnifying power is large.
(iii) Resolving power is large.
(iv) Spherical aberration is reduced.
(v) Free from chromatic aberration.
OR
(a) Definition of wave front Verification of laws of reflection
(b) Explanation of the effect on the size and intensity of central maxima
(c) Explanation of the bright spot in the shadow of the obstacle
(a) The wave front may be defined as a surface of constant phase.
(Alternatively: The wave front is the loci of all points that are in the same phase.)
Let the speed of the wave in the medium be '
Let the time taken by the wave front, to advance from point
Hence
Let
Distance
(b) Size of central maxima reduces to half,
Intensity increases.
This is because the amount of light, entering the slit, has increased and the area, over which it falls, decreases.
(Also accept if the student just writes that the intensity becomes four fold.)
(c) This is because of diffraction of light.
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