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Ray And Wave Optics Mcq
Quiz 10
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Q.1
Consider Fraunhofer diffraction pattern obtained with a single slit, illuminated at normal incidence. At the angular position of the first diffraction minimum, the phase difference ( in radians ) between the wavelets from the opposite edges of the slit is [ IIT 1995]
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a) π
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b) 2π
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c)π/4
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d)π/2
Explanation
First minima in single slit experiment lies between +π and -π Therefore the required answer is=π - ( -π)=2πAnswer: (b)
Q.2
In double slit experiment, the angular width of the fringes is 0.2° for sodium light ( λ=5890Å ) . In order to increase the fringe width by 10% the necessary change in the wavelength is [ MPPMT 1997]
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a) increase of 589Å
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b) decrease of 589Å
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c)increase of 6479Å
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d)zero
Explanation
We know that θ=λ/d θ2=0.22° λ2 - λ1=589Å Answer:(a)
Q.3
A beam of light AO is incident on a glass slab ( µ=1.54) in a direction as shown in the adjoining diagram. The reflected ray OB is passed through a Nicol prism. On viewing through the Nicol prism, we find on rotating the prism that ( given tan57°=1.54) [ CPMT 1986]
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a) The intensity is reduced down ro zero and remains zero
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b) The intensity reduces down some what and rises again
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c) there is no change in intensity
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d) The intensity gradually reduces to zero and then again increases
Explanation
Angle of incidence is 57° According to Brewester law if tani=µ then reflected ray's are plane polarized. In given problem condition is satisfied thus reflected ray's are plane polarized Answer: (d)
Q.4
In double slit experiment, for light of which colour the fringe width will be minimum [ MPPMT 1994]
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a)Violet
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b) Red
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c)Green
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d)Yellow
Explanation
Answer: (a)
Q.5
While both light and sound shows wave character, diffraction is much higher to observe in light. This is because [ CET 1994]
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a) light does not require a medium
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b) wavelength of light is far smaller
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c)waves of light are transverse
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d)speed of light is far greater
Explanation
Answer: (b)
Q.6
Find the thickness of plate which will produce a change in optical path equal to half the wavelength Λ of light passing through it, normally. The refractive index of the plate is µ [ CPMT 1998]
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a)λ / [4(µ - 1)]
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b) 2λ / [4(µ - 1)]
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c)λ / (µ - 1)
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d)λ / [2(µ - 1)]
Explanation
path difference=(µ - 1) t λ/2=(µ - 1) t t=λ/[2(µ - 1)] Answer:(d)
Q.7
In the adjoining diagram, wavefront AB, moving in air is incident on a plane glass surface XY. Its position CD after refraction through a glass slab is shown also along with the normal's drawn at A and D. The refractive index of glass with respect to air (µ ) will be equal to{( CPMT 1988]
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a) sinθ/sinθ'
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b) sinθ/sinφ'
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c) sinφ'/sinθ
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d) AB /CD
Explanation
From geometry of figure and Snell's law Answer: (b)
Q.8
A thin oil layer floats on water. A ray of light making an angle of incidence of 40° shines on oil layer. The angle of refraction of ray with water surface is ( µoil=1.45, µwater=1.33) [MPPMT 1993]
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a)36.1°
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b) 44.5°
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c)26.8 °
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d)28.9°
Explanation
from figure 1.47=sin40 / sinr1 sinr1=0642 / 1.45 r1=0.642 / 1.45 r1=26.31° 1.33/1.45=sinr1 / sin r2 r2=29°Answer: (d)
Q.9
Four different independent waves are represented by i) y1=a1sinωtii) y2=a2sin2ωtiii) y3=a3cosωtiv) y4=a4sin(ωt+π/3) with which of two waves, interference is possible
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a) in (i) and (ii)
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b) in (i) and (iv)
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c)in (iii) and (iv)
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d)not possible with any combination
Explanation
Answer: (d)
Q.10
The refracting angle of prism is A and refractive index of material of prism is cot(A/2). The angle of minimum deviation is
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a) (180° - 3A)
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b) (180° + 2A)
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c)( 90° - A)
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d)(180° - 2A)
Explanation
Answer:(d)
Q.11
A disc is placed on a surface of pond which has refractive index 5/A source of light is placed 4m below the surface of the liquid. The minimum radius of disc needed so that light is not coming out is [ CBSE 2001]
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a)∞
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b) 3m
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c)6 m
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d)4 m
Explanation
For total internal reflection θ must be equal to critical angle µ=1 / sinC From figure Answer: (b)
Q.12
A camera objective has an aperture diameter d. If the aperture is reduced to diameter d/2, the exposure time under identical condition of light should be made [ KErala, PMT 2004]
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a) √2 fold
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b) 2 fold
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c)2√2 fold
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d)4 fold
Explanation
When aperture is reduced to half area becomes 1/4th. Therefore, exposure time should be made 4 foldAnswer: (d)
Q.13
In a compound microscope, the objective lens of fo and eye piece of fe are placed at distance L such that L equals [ kerala P.M.T 2004]
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a)fo + fe
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b) fo - fe
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c)much greater than fo or fe
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d)much less than fo or fe
Explanation
Answer:(a)
Q.14
A single slit is located effectively at infinity in front of lens of focal length 1m, and it is illuminated normally with light of wavelength 600nm. The first minimum on either side of central maximum are separated by 4mm. Width of the slit is [ Kerala PMT 2004]
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a) 0.1 mm
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b) 0.2 mm
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c) 0.3 mm
0%
d) 0.4 mm
Explanation
Here f=D=1 m, given 2w=4 mm , x=2mm width of fringe x=Dλ /d d=Dλ /x d=1×6×107 / 2×10-3 d=3×10-4=0.3mm Answer: (c)
Q.15
The dispersive power of the material of lens of focal length 20cm is 0.The longitudinal chromatic aberration of the lens is [ kerala PMT 2004]
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a)0.08 cm
0%
b) 1.6 cm
0%
c)0.08/20 cm
0%
d)0.16 cm
Explanation
Longitudinal chromatic aberration=ωf=0.08×20=1.6 cmAnswer: (b)
Q.16
A ray of light passes through an equilateral prism such that angle of incidence is equal to the angle of emergence and the latter is equal to 3/4th angle of prism. The angle of deviation is [ Kerala PET 2004]
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a) 45°
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b) 39°
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c)20°
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d)30°
Explanation
When i=e, prism is in minimum deviation position i=e=(3/4)A=(3/4)×60°=45° δm=2i - A δm=2×45 - 60=30°Answer: (d)
Q.17
In a compound microscope, the intermediate image is [ kerala PEt 2004]
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a) virtual, erect and magnified
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b) real, erect and magnified
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c)real, inverted and magnified
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d)virtual, ere and magnified
Explanation
Answer:(c)
Q.18
A fish at depth of 12cn in water is viewed by an observer on the bank of lake. Through what height is the image of fish raised [µ=4/3) )kera PET 2004]
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a) 9 cm
0%
b) 12 cm
0%
c) 3 cm
0%
d) 3.8 cm
Explanation
µ=real depth / apparent depth 4/3 12/ x x=9 cm The height through which image of fish is raised=12 - 9=3 cm Answer: (c)
Q.19
Two plane mirrors are arranged at right angles to each other as shown in figure. A ray of light is incident on the horizontal mirror at an angle Θ. For what value of θ the ray emerges parallel to the incoming ray after reflection from the vertical mirror?
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a)75°
0%
b) 45°
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c) 30°
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d)all of the above
Explanation
Answer: (d)
Q.20
A concave mirror has focal length 20cm. The distance between the two position of object for which the image size i doubled the object size is
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a) 20 cm
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b) 40 cm
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c)30 cm
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d)60 cm
Explanation
For real image u=-u1 then form the formula for magnification v==-2u1 f=-20 cm Substituting the data in mirror formula we get u1=30 cm For virtual image u=-u2 , and v=2u2 f=-20 cm Substituting the data in mirror formula we get u2=10 cm Distance between two position of the object=u1 -u2=20 cmAnswer: (a)
Q.21
One side of the glass slab is silvered as shown. A ray of light is incident on the other side at an angle of incidence i=45°. Refractive index of glass is given as 1.The deviation of the ray of light from its initial path when it comes out of slab is
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a) 90°
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b) 180°
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c)120°
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d)45°
Explanation
Answer:(a)
Q.22
A thin prism with angle 4° and refractive index 1.5 is placed inside a transparent tube with water ( refractive index=5/4) as shown. The deviation of light due t prism will be
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a) 0.8° upward
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b) 0.8° downward
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c) 0.67° upward
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d) 0.37° downward
Explanation
Let µ1 be the refractive index of prism and µ2 be the refractive index of water Answer: (b)
Q.23
A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index µ=1.5 as shown in figure. The position of the image formed by the refraction at the spherical surface only is
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a)R/2
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b) 3R
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c)R/3
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d)2R
Explanation
Object is at infinity, and image is in glass use formula form refraction at curved surface Answer: (b)
Q.24
A man approaches a vertical plane mirror at speed of 2m/s. Then the rate at which he approaches his image is
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a) 2 m/s
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b) 4m/s
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c)1 m/s
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d)zero
Explanation
Answer: (b)
Q.25
A ray of light falls on the surface of a spherical glass paper-weight making an angle α with normal and is refracted in the medium at an angle β. The angle of deviation of emergent ray from the direction of the incident ray is
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a) (α - β)
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b) 2(α - β)
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c)(α - β) / 2
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d)(α + β)
Explanation
from figure δ=2(α - β) Answer:(b)
Q.26
If white light is used in a Young's double slit experiment
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a) bright white fringe is not formed at the centre of the screen
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b) fringes of different colurs are not observed clearly only in the first order
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c) the first-order violet fringe is closer to the central fringe than the first-order red fringe
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d) the first order red fringe is closer to the central fringe than the first-order violet fringe
Explanation
With white light only central fringe is white As λviolet < λred Position of fringe X=Dnλ / d Xviolet < Xred Condition for constructive interference is satisfied by violet first and the red. The violet fringe will be next to central fringe Answer: (c)
Q.27
A thin lens of focal length f produces an upright image of same size as the object. What is the distance of the object from the optical centre of the lens?
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a)2f
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b) zero
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c)3f/2
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d)infinity
Explanation
v=mu given m=1 v=u is possible for convex lens only if v=u=0Answer: (b)
Q.28
Two thin lenses, one concave and the other is convex are placed in contact with each other. If their powers are in the ratio 2/3 and the effective focal length of the combination is 30cm, then the individual focal lengths are
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a) -75 cm, +50 cm
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b) -15 cm, 10cm
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c)+75cm, -50cm
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d)75cm, 50cm
Explanation
on simplification of above equations focal length of concave lens=-15cm and focal length of convex lens=+10cmAnswer: (b)
Q.29
Two identical sources P and Q emit waves in same phase and same wavelength. Spacing between P and Q is 3λ. The maximum distance from P along the x-axis at which a minimum intensity occurs is given by
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a) 6.58λ
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b) 2.25λ
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c)8.75λ
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d)055λ
Explanation
On the horizontal, the path difference is decreasing on increasing X . so at the maximum distance from point P where minima occurs, path difference is λ/2 from geometry of figure Answer:(c)
Q.30
Interference pattern is obtained by using light having two wave lengths 400nm and 560nm. The light falls normally on two narrow slits. The distance between the successive regions of "Total Darkness' is
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a) 4 mm
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b) 5.6 mm
0%
c) 14mm
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d) 28mm
Explanation
region between Total Darkness is bright fringe At a point constructive interference of both should overlap by using formula Answer: (d)
Q.31
The refractive index of material varies with wavelength according to the Cauch's relation is
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a) µ=A λ + B
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b) µ=A + B / λ2
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c)µ=A × B / λ
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d)µ=A2λ + B
Explanation
Answer: (b)
Q.32
Indicate the correct statement in the following
0%
a)The dispersive power depends upon the angle of prism
0%
b) The angular dispersion depends upon the angle of the prism
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c)the angular dispersion does not depend upon the dispersive power
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d)the dispersive power in vacuum is one
Explanation
Answer: (b)
Q.33
A ray of light falls normally on a refracting face of a prism of refractive index 1.What is the angle of prism if the ray just fails to emerge from the prism?
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a)30°
0%
b) sin-1 (1/3)
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c)tan-1 (3/2)
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d)none of these
Explanation
For total internal reflection at face AB.A=r1 + r2 r1=0 on Ac ∴ r2=ABut r2 > C (Critical angle) sinA > 1 /µsinA > (2/3) Answer: (d)
Q.34
Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index µ is placed on the face AC of the prism. The prism is made of glass of refractive index 3/The limits of µ for which total internal reflection takes place on face AC is
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a) µ > √3 /2
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b) µ < 3√3 /4
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c)µ > √3
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d)µ < √3 /2
Explanation
Angle of incidence on face AC=60°For total internal reflection angle of incidence on face AC sinθ > (3/2)/µ sin60 > 2µ/3 √3 / 2 > 2µ/33√3 / 4 > µµ < 3√3 / 4Answer: (b)
Q.35
A ray of light passing through a prism of refracting angle 60° has to deviate by at least 30°. Then refractive index of prism should be
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a) ≤ √2
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b) ≥ √2
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c)≥ √3
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d)≤ √3
Explanation
Use formula On simplification we get µ=√2, At µ=√2, minimum deviation is 30°, for δ ≥ 30°, µ ≥ √2 Answer:(b)
Q.36
An object is kept at a distance of 16 cm from a think lens and the image formed is real. If the object is kept at distance of 6cm from the same lens, the image formed is virtual. If the size of the images formed are equal, the focal length of the lens will be
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a) 15 cm
0%
b) 17 cm
0%
c) 21 cm
0%
d) 11 cm
Explanation
Real image is formed only by convex lens u=-16 cm if n is magnification then v=16n applying lens equation we get second case u=-6 cm v=-6n ( as magnification is same in both cases) adding (1) and (2) we get 2=22/f or f=11cmAnswer: (d)
Q.37
Young's double slit experiment is made in liquid. the 10th bright fringe lies in liquid where 6th dark fringe lies in vacuum. The refractive index of the liquid is approximately.
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a)1.8
0%
b) 1.5
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c)1.3
0%
d)1.6
Explanation
Position of fringe in both case is same use formula for dark and bright fringeLet refractive index of liquid be Let wave length of light in liquid be λ'=λ/µ Answer: (a)
Q.38
In Young's double slit experiment how many maximas can be obtained on a screen ( including central maximum) on both sides of the central fringe, if λ=2000Å and d=7000Å. Given that perpendicular distance of screen from the mid point of two slits is 3.5 cm
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a) 12
0%
b) 7
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c)18
0%
d)4
Explanation
For maximum intensity on the screendsinθ=nλ sinθ=nλ/d Since can have maximum value=1nλ/d=1 n=d/ λ=7000 / 2000=3.5 thus n=3 that is 3 bright fringe up three down total fringes seven including central maximaAnswer: (b)
Q.39
A plastic hemisphere has a radius of curvature of 8cm and an index of refraction of 1.On the axis half way between the plane surface and the spherical one ( 4 cm from each) is small object O. The distance between the two images when viewed along the axis from the two sides of the hemisphere is approximately
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a) 1.0 cm
0%
b) 1.5 cm
0%
c)3.75 cm
0%
d)2.5 cm
Explanation
Distance of image from plane surface is distance apparent=distance actual / µ x1=4/1.5=2.5 cm Distance of image from curved surface ( use formula for refraction at curved surface) negative sign indicates image is on object side Distance between images=( 8 - 2.5 -3)=2.5 cm Answer:(d)
Q.40
A ray is incident on a medium consisting of two boundaries, one plane and other curved as shown in figure . The plane surface makes an angle of 60° with horizontal and curved surface has radius of curvature 0.4m. The refractive indices of the medium and its environment are shown in the figure. If after refraction at both the surfaces the ray meets the principle axis at P, find OP
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a) 2.056 m
0%
b) 5.056 m
0%
c) 6.056 m
0%
d) 4.056 m
Explanation
Applying Snell's law at face AB 1×sin45=√2 ×sinr ∴ r=30° Refracted ray will be parallel to the face AD as shown in figure Now refraction at spherical surface u=∞ ( as incident ray is parallel to principal axis ) Answer: (c)
Q.41
A ray of light is incident on a glass sphere of refractive index 3/What should be the angle of incidence so that the ray which enters the sphere comes out tangentially from the surface of the sphere
0%
a)tan-1(2/3)
0%
b) sin-1(2/3)
0%
c)90°
0%
d)cos-1(1/3)
Explanation
As shown in figure ∠ABO=∠OAB=θApplying snells law at A sini=sinθ(3/2) --eq(1)Applying Senll's law at B (3/2)sinθ=sin90 sinθ=2/3 --eq(2)from equation (1) and (2) sini=(2/3)(3/2)=1 thus i=90°Answer: (c)
Q.42
A plane mirror is made of glass slab (µg=1.5), 2.5 cm thick and silvered on the back. A point object is placed 5cm in front of the unsilvered face of the mirror. What will be the position of final image?
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a) 12 cm from unsilvered face
0%
b) 14.6 cm from unsilvered face
0%
c)5.67 cm from unsilvered face
0%
d)8.33 cm from unsilvered face
Explanation
As shown in figure I2 : Image formed due to reflection from DEFI3 : Image form due to refraction from ABCObject distance for face DEF Thus image I2=7.5 +2.5=10cm behind face DFF This image will act as object , distance from face ABC=10+2.5=12.5 image is behind the unsilvered faceAnswer: (d)
Q.43
The maximum intensity in Young's double slit experiment is Io. Distance between the slits is d=5λ, where λ is the wave length of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on screen at a distance D=10d?
0%
a) Io /2
0%
b) (3/4)Io
0%
c)Io
0%
d)Io/4
Explanation
Position of point onscreen x then path difference=xd/D Here point is at distance x=d/2 to make it infrant of one of the slit given d=5λ and D=10d=50λCorresponding phase difference φ=π/2From the formula for intensity when Io is maximum intensity Answer:(a)
Q.44
In Young's double slit experiment d/D=10-At a point P on the screen the resulting intensity is equal to the intensity due to individual slit Io. Then the distance of point P from the central maxima is ( λ=6000Å)
0%
a) 2 mm
0%
b) 1 mm
0%
c) 0.5 mm
0%
d) 4 mm
Explanation
If Io is intensity due to individual slit then From the formula for Intensity at point, Path difference for 2π /3=Λ/3 But Path difference=xd/D Answer: (a)
Q.45
If the critical angle for the medium of prism is C and the angle of the prism is A, then there will be no emergent ray when
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a) A < 2C
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b) A=2C
0%
c)A > 2C
0%
d)A >=< 2C
Explanation
Answer:(c)
Q.46
Longitudinal chromatic aberration is given by
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a) ω + f
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b) ω × f
0%
c)ω / f
0%
d)ω f2
Explanation
Answer: (b)
Q.47
A point object is placed at a distance of 25cm from a convex lens of focal length 20cm. If a glass slab of thickness to and refractive index 1.5 is inserted between the lens and the object the image is formed at infinity, the thickness t is
0%
a)10 cm
0%
b) 5 cm
0%
c)20 cm
0%
d)15 cm
Explanation
Image will be form at infinity if object is placed at focus of the lens. That is 20 cm from the lensThus shift=25 -20=5Formula for shift=[ 1- (1/µ)]tf=[ 1 - (1/1.5)]t t=15 cmAnswer: (d)
Q.48
lens of glass (µg=1.5) of focal length 10 cm is silvered on one side. It will behave like a
0%
a) a) concave mirror of focal length 10 cm
0%
b) convex mirror of focal length 5.0 cm
0%
c)concave mirror of focal length 2.5 cm
0%
d)convex mirror of focal length 20 cm
Explanation
For equiconvex lens |R1|=|R2|=f=10 cm Therefore, the system will behave like concave mirror of focal length 2.5 cmAnswer: (c)
Q.49
A point object O is placed at a distance of 20cm from a convex lens of focal length 10cm as shown in figure. At what distance x from lens should a convex mirror of focal length 60 cm, be laced so that final image coincides with object?
0%
a) 10 cm
0%
b) 40 cm
0%
c)20 cm
0%
d)final image can never coincide with the object under the given condition
Explanation
Object is placed at distance 2f from the lens . the image is formed at 2f or 2 cm from lens. So, if the convex mirror is placed at 20 cm from lens , the first image formed by lens will be at the pole of mirror and it will reflect all the rays symmetrically to other side as shown in figure and the final image will coincide with the object Answer:(c)
Q.50
A monochromatic beam of light falls on Young's double slit Experiment apparatus at some angle as shown in figure.A thin sheet of glass is inserted in front of the lower slit SThe central bright fringe will be obtained
0%
a) at O
0%
b) above O
0%
c) below O
0%
d) anywhere depending on thickness of plate angle and refractive index of glass
Explanation
If path difference dsinθ=(µ - 1) t, central fringe is obtained at O If dsinθ > (µ - 1) t, central fringe is obtained above O If dsinθ < (µ - 1) t, central fringe is obtained below OThus fringe position depends on thickness of plate angle and refractive index of glass Answer: (d)
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