JEE Main & Advanced Physics Ray Optics Sample Paper

done Topic Test - Refraction of Light Through Plane Surfaces Total Questions - 35    [Download]

• question_answer1)
  What happens to light as it passes from glass into air?
  A)
  Its frequency decreases because its speed decreases
  done clear
  B)
  Its frequency increases because its speed increases.
  done clear
  C)
  Its wavelength decreases because its speed decreases
  done clear
  D)
  Its wavelength increases because its speed increases
  done clear
  View Answer play_arrow

• question_answer2)
  The curve of angle of incidence versus angle of deviation shown has been plotted of prism. The value of refractive index of the prism used is:
  A)
  \[\sqrt{3}\]
  done clear
  B)
  \[\sqrt{2}\]
  done clear
  C)
  \[\frac{\sqrt{3}}{\sqrt{2}}\]
  done clear
  D)
  \[\frac{2}{\sqrt{3}}\]
  done clear
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• question_answer3)
  In the given curve of the above question, find the value of angle \[{{i}_{1}}\] in degrees.
  A)
  \[{{40}^{o}}\]         
  done clear
  B)
  \[{{60}^{o}}\] 
  done clear
  C)
  \[{{70}^{o}}\]
  done clear
  D)
  \[{{90}^{o}}\]
  done clear
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• question_answer4)
  A ray of light passes from vacuum into a medium of refractive index \[\mu ,\] the angle of incidence is found to be twice the angle of refraction. Then the angle of incidence is
  A)
  \[{{\cos }^{-1}}(\mu /2)\]
  done clear
  B)
  \[2{{\cos }^{-1}}(\mu /2)\]
  done clear
  C)
  \[2{{\sin }^{-1}}(\mu )\]
  done clear
  D)
  \[2{{\sin }^{-1}}\,(\mu /2)\]
  done clear
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• question_answer5)
  A vertical microscope is focused on a point at the bottom of an empty tank. Water \[\left( \mu =\frac{4}{3} \right)\] is then poured into the tank. The height of the water column is 4 cm. Another lighter liquid, which does not mix with water and which has refractive index \[\frac{3}{2}\] is then poured over the water. The height of liquid column is 2 cm. What is the vertical distance through which the microscope must be moved to bring the object in focus again?
  A)
  2.61 m
  done clear
  B)
  1.55 m
  done clear
  C)
  3.12 m
  done clear
  D)
  1.67 m
  done clear
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• question_answer6)
  A prism of dispersive power 0.021 and refractive index 1.53 form an achromatic combination with prism of angle \[4.2{}^\circ \] and dispersive power 0.045 having refractive index 1.65. Find the resultant deviation.
  A)
  \[1.12{}^\circ \]
  done clear
  B)
  \[2.16{}^\circ \]
  done clear
  C)
  \[3.12{}^\circ \]
  done clear
  D)
  \[4.18{}^\circ \]
  done clear
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• question_answer7)
  A ray incident at a point at an angle of incidence of \[{{60}^{o}},\] enters a glass sphere of refractive index \[n=\sqrt{3}\] and is reflected and refracted at the further surface of the sphere. The angle between the reflected and refracted rays at this surface is
  A)
  \[50{}^\circ \]
  done clear
  B)
  \[60{}^\circ \]
  done clear
  C)
  \[90{}^\circ \]
  done clear
  D)
  \[40{}^\circ \]
  done clear
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• question_answer8)

  A glass prism is immersed in a hypothetical liquid. The curves showing the refractive index n as a function of wavelength \[\lambda \] for glass and liquid are as shown in the figure. A ray of white light is incident on the prism parallel to the base. Choose the incorrect statement -

  A)
  yellow ray travels without deviation
  done clear
  B)
  blue ray is deviated towards the vertex
  done clear
  C)
  red ray is deviated towards the base
  done clear
  D)
  there is no dispersion
  done clear
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• question_answer9)

  A horizontal ray of light passes through a prism of \[\mu =1.5\] whose apex angle is \[4{}^\circ \] and then strikes a vertical mirror M as shown. For the ray after reflection to become horizontal, the mirror must be rotated through an angle of:

  A)
  \[{{2}^{o}}\]
  done clear
  B)
  \[{{3}^{\text{o}}}\]
  done clear
  C)
  \[{{4}^{\text{o}}}\]
  done clear
  D)
  \[{{1}^{\text{o}}}\]
  done clear
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• question_answer10)
  A light wave travels from glass to water. The refractive index for glass and water are \[\frac{3}{2}\] and \[\frac{4}{3}\] respectively. The value of the critical angle will be:
  A)
  \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
  B)
  \[{{\sin }^{-1}}\left( \frac{9}{8} \right)\]
  done clear
  C)
  \[{{\sin }^{-1}}\left( \frac{8}{9} \right)\]
  done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{5}{7} \right)\]
  done clear
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• question_answer11)

  A cylinderical optical fibre (quarter circular shape) of refractive index \[n=2\] and diameter \[d=4\text{ }mm\] is surrounded by air. A light beam is sent into the fibre along its axis as shown in figure. Then the smallest outer radius R (as shown in figure) for which no light escapes after first incident on curved surface of fibre is:

  A)
  2 mm
  done clear
  B)
  4 mm
  done clear
  C)
  8 mm
  done clear
  D)
  6 mm
  done clear
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• question_answer12)
  The refractive index of air is 1.0003. The thickness of air column which will have one more wavelength of yellow light \[(X=\text{ }6000\overset{o}{\mathop{A}}\,)\] than in the same thickness in vacuum is
  A)
  2 mm
  done clear
  B)
  2 cm
  done clear
  C)
  2 m
  done clear
  D)
  2 km
  done clear
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• question_answer13)
  A light beam is travelling from Region I to Region IV (Refer Figure). The refractive index in Regions I, II, III and IV are \[{{n}_{0}},\,\frac{{{n}_{0}}}{2},\,\frac{{{n}_{0}}}{6}\] and \[\frac{{{n}_{0}}}{8},\] respectively. The angle of incidence 6 for which the beam just misses entering Region IV is

  Region I		Region II		Region III		Region IV
  		\[\frac{{{n}_{0}}}{2}\]		\[\frac{{{n}_{0}}}{6}\]		\[\frac{{{n}_{0}}}{8}\]
  	0		0.2 m		0.6 m

  A)
  \[{{\sin }^{-1}}\left( \frac{3}{4} \right)\]
  done clear
  B)
  \[{{\sin }^{-1}}\left( \frac{1}{8} \right)\]
  done clear
  C)
  \[{{\sin }^{-1}}\left( \frac{1}{4} \right)\]            
  done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{1}{3} \right)\]
  done clear
  View Answer play_arrow

• question_answer14)
  Minimum number of prisms required to make a combination which is 'Achromatic' as well as 'Direct Vision' is:
  A)
  2
  done clear
  B)
  3
  done clear
  C)
  4
  done clear
  D)
  11
  done clear
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• question_answer15)

  In the figure [a] the light is incident at an angle \[{{\mu }_{k}}=1-\frac{1}{{{n}^{2}}}\] (slightly greater than the critical angle). Now keeping the incident ray fixed a parallel slab of refractive index \[{{n}_{3}}\] is placed on surface AB.

  A)
  total internal reflection occurs at AB for \[{{n}_{3}}={{n}_{2}}\]  
  done clear
  B)
  total internal reflection occurs at AB for \[{{n}_{3}}>{{n}_{1}}\]
  done clear
  C)
  the ray will return back to the same medium for all values of \[{{n}_{3}}\]
  done clear
  D)
  total reflection occurs at CD for \[{{n}_{3}}<{{n}_{1}}\].
  done clear
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• question_answer16)
  A beam of monochromatic light is incident at \[i={{50}^{o}}\] on one face of an equilateral prism the angle of emergence is \[40{}^\circ ,\] then the angle of minimum deviation is-                   
  A)
  \[{{30}^{o}}\]         
  done clear
  B)
  \[<{{30}^{o}}\]
  done clear
  C)
  \[\le {{30}^{o}}\]
  done clear
  D)
  \[\ge {{30}^{o}}\]
  done clear
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• question_answer17)
  The critical angle of light going from medium A to medium B is \[\theta \]. The speed of light in medium A is v. The speed of light in medium B is:
  A)
  \[\frac{v}{\sin \theta }\]
  done clear
  B)
  \[v\,\,\sin \theta \]
  done clear
  C)
  \[v\,\,\cot \theta \]
  done clear
  D)
  \[v\,\,\tan \theta \]
  done clear
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• question_answer18)

  r and r? denote the angles inside an equilateral prism, as usual, in degrees. Consider that during some time interval from \[t=0\] to \[t=t,\,r'\] varies with time as \[r'=10+{{t}^{2}}.\] During this time r will vary as: (Assume that r and r? are in degree):

  A)
  \[50-{{t}^{2}}\]
  done clear
  B)
  \[50+{{t}^{2}}\]
  done clear
  C)
  \[60-{{t}^{2}}\]
  done clear
  D)
  \[60+{{t}^{2}}\]
  done clear
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• question_answer19)
  One of the refracting surface of a prism of refractive index \[\sqrt{2}\] is silvered. The angle of the prism is equal to the critical angle of a medium of refractive index 2. A ray of light incident in the silvered surface passes through the prism and retraces its path after reflection at the silvered face. Then the angle of incidence on the un silvered surface is
  A)
  \[{{0}^{o}}\]
  done clear
  B)
  \[{{30}^{o}}\]
  done clear
  C)
  \[{{45}^{o}}\]
  done clear
  D)
  \[{{60}^{o}}\]
  done clear
  View Answer play_arrow

• question_answer20)
  A plane mirror is made of glass slab \[({{\mu }_{g}}=1.5)\,2.5\,\text{cm}\] thick and silvered on the back. A point object is placed 5 cm in front of the unsilvered face of the mirror. What will be the position of final image:
  A)
  12 cm from front face                        
  done clear
  B)
  14.6 cm from front face
  done clear
  C)
  5.67 cm from front face                      
  done clear
  D)
  8.33 cm from front face
  done clear
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• question_answer21)

  A transparent solid cylindrical rod has a refractive index of \[\frac{2}{\sqrt{3}}\]. It is surrounded by air. A light ray is incident at the mid-point of one end of the rod as shown in the figure.

  The incident angle \[(\theta )\] for which the light ray grazes along the wall of the rod is:

  A)
  \[{{\sin }^{-1}}\left( \frac{\sqrt{3}}{2} \right)\]
  done clear
  B)
  \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
  done clear
  C)
  \[{{\sin }^{-1}}\left( \frac{1}{\sqrt{3}} \right)\]
  done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{1}{2} \right)\]
  done clear
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• question_answer22)

  It is found that all electromagnetic signals sent from A towards B reach point C. The speed of electromagnetic signals in glass cannot be:

  A)
  \[1.0\times {{10}^{8}}m/s\]
  done clear
  B)
  \[2.4\times {{10}^{8}}m/s\]
  done clear
  C)
  \[2\times {{10}^{7}}m/s\]
  done clear
  D)
  \[4\times {{10}^{7}}m/s\]
  done clear
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• question_answer23)

  A ray hits the y-axis making an angle \[\theta \] with y-axis as shown in the figure. The variation of refractive index with x-coordinate is \[\mu ={{\mu }_{0}}\left( 1-\frac{x}{d} \right)\] for \[0\le \times \le d\left( 1-\frac{1}{{{\mu }_{0}}} \right)\] and \[\mu ={{\mu }_{0}}\] for \[x<0\] where d is a positive constant. The maximum x-coordinate of the path traced by the ray is

  A)
  \[d(1-\sin \theta )\]
  done clear
  B)
  \[d(1-\cos \theta )\]
  done clear
  C)
  \[d\,\,\sin \theta \]
  done clear
  D)
  \[d\,\,\cos \theta \]
  done clear
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• question_answer24)

  An isosceles trapezium of reflecting material of refractive index \[\sqrt{2}\] and dimension of sides being 5 cm, 5 cm, 10 cm and 5 cm. The angle of minimum deviation by this when light is incident from air and emerges in air is:

  A)
  \[22\frac{1}{2}{}^\circ \]
  done clear
  B)
  \[\text{45}{}^\circ \]
  done clear
  C)
  \[\text{3}0{}^\circ \]
  done clear
  D)
  \[\text{6}0{}^\circ \]
  done clear
  View Answer play_arrow

• question_answer25)

  A man is standing at the edge of a 1 m deep swimming pool, completely filled with a liquid of refractive index \[\sqrt{3/2}\]. The eyes of the man are \[\sqrt{3}m\] above the ground. A coin located at the bottom of the pool appears to be at an angle of depression of \[\text{3}0{}^\circ \] with reference to the eye of man. Then horizontal distance (represented by \[\times \] in the figure) of the coin from the eye of the man is .....   mm.

  A)
  2000
  done clear
  B)
  3000             
  done clear
  C)
  4000
  done clear
  D)
  8000
  done clear
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• question_answer26)

  Statement-1: Beam of white light is incident on a transparent glass hemisphere as shown in figure. The beam is rotated clockwise so that angle \[\theta \] increases, as the refracted beam approaches a direction parallel to the horizontal it appears red.

  Statement-2: Critical angle for a pair of medium depends on \[Rl's\] of mediums and given by \[{{i}_{c}}={{\sin }^{-1}}\left( \frac{1}{_{R}{{\mu }_{D}}} \right)\And Rl\] in turn depends on wavelength of light.

  A)
  Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
  done clear
  B)
  Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for Statement-1
  done clear
  C)
  Statement-1 is True, Statement -2 is False
  done clear
  D)
  Statement -1 is False, Statement-2 is True
  done clear
  View Answer play_arrow

• question_answer27)
  Match List-I (Phenomenon) with List-II (Principle) and select the correct answer using the codes given below the lists

  List - I		List - II
  I.	Blue color of a sky	A.	Total internal reflection
  II.	Glittering of diamond	B.	Dispersion of light
  III.	Formation of rainbow	C.	Scattering of light
  IV.	In the evening when the sun goes down blow the horizon, it continues to remain visible for some time	D.	Refraction of light

  Codes:
  A)
  I - C, II - A, III - B, IV - D
  done clear
  B)
  I - C, II - A, III - D, IV - B
  done clear
  C)
  I - A, II - C, III - B, IV - D
  done clear
  D)
  I - A, II - C, III - D, IV - B
  done clear
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• question_answer28)
  A point source of light is placed at a distance h below the surface of a large deep lake. What is the percentage of light energy that escapes directly from the water surface if \[\mu \] of water \[=\frac{4}{3}\]?
  A)
  50%
  done clear
  B)
  25%
  done clear
  C)
  20%
  done clear
  D)
  17%
  done clear
  View Answer play_arrow

• question_answer29)
  If the signal is transmitted from an optical fibre core of Refractive Index (RI) \[\sqrt{\frac{12}{5}}\] to an another optical fibre with RI of core and cladding as 1.8 and 1.2 respectively, then the maximum angle of acceptance for 2nd optical fibre is
  A)
  \[30{}^\circ \]
  done clear
  B)
  \[45{}^\circ \]
  done clear
  C)
  \[60{}^\circ \]
  done clear
  D)
  \[{{\sin }^{-1}}\left( \frac{2}{\sqrt{3}} \right)\]
  done clear
  View Answer play_arrow

• question_answer30)
  A man in an empty swimming pool has a telescope focused at 4'O clock sun. When the swimming pool is filled with water, the man (now inside the water with his telescope undisturbed) observes the setting sun. Find the refractive index of water, if sun rises and sets at 6'O clock.
  A)
  \[\frac{4}{3}\]
  done clear
  B)
  \[\frac{2}{\sqrt{3}}\]
  done clear
  C)
  \[\frac{8}{5}\]
  done clear
  D)
  \[\frac{2}{5}\]
  done clear
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• question_answer31)
  If \[{{\mu }_{1}}\] and \[{{\mu }_{2}}\] are the refractive indices of the materials of core and cladding of an optical fibre, then the loss of light due to its leakage can be minimised by having
  A)
  \[{{\mu }_{1}}>{{\mu }_{2}}\]
  done clear
  B)
  \[{{\mu }_{1}}<{{\mu }_{2}}\]            
  done clear
  C)
  \[{{\mu }_{1}}={{\mu }_{2}}\]
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer32)

  A glass slab of width 't', refractive index \['\mu '\] is placed as shown in the figure. If the point object, moves with a speed 2 cm/sec towards the slab the observed speed by the observer will be :

  A)
  2 cm/sec                     
  done clear
  B)
  less than 2 cm/sec
  done clear
  C)
  greater than 2 cm/sec                    
  done clear
  D)
  \[(2/\mu )\] cm/sec
  done clear
  View Answer play_arrow

• question_answer33)

  Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index 3/2 is placed on face AC of the prism. The prism is made of glass of refractive index 3/2. The limits of \[\mu \]for which total internal reflection cannot take place on face AC is

  A)
   \[\frac{3\sqrt{3}}{4}>\mu >\frac{\sqrt{3}}{2}\]
  done clear
  B)
  \[\mu <\frac{3\sqrt{3}}{4}\]
  done clear
  C)
  \[\mu >\sqrt{3}\]
  done clear
  D)
  \[\mu <\frac{\sqrt{3}}{2}\]
  done clear
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• question_answer34)
  A glass slab has the left half of refractive index \[{{n}_{1}},\] and the right half of \[{{n}_{2}}=3{{n}_{1}}\]. The effective refractive index of the whole slab is
  A)
  \[\frac{{{n}_{1}}}{2}\]
  done clear
  B)
  \[2n\]
  done clear
  C)
  \[\frac{3{{n}_{1}}}{2}\]
  done clear
  D)
  \[\frac{2{{n}_{1}}}{3}\]
  done clear
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• question_answer35)
  Let the \[x-y\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has refractive index of \[\sqrt{2}\] and medium 2 with \[z<0\] has a refractive index of \[\sqrt{3}\]. A ray of light in medium 1 given by the vector \[\vec{A}=6\sqrt{3}\hat{i}+8\sqrt{3}\,\hat{j}-10\hat{k}\] is incident on the plane of separation. The angle of refraction in medium 2 is
  A)
  \[{{30}^{o}}\]         
  done clear
  B)
  \[{{45}^{o}}\]
  done clear
  C)
  \[{{60}^{o}}\]  
  done clear
  D)
  \[{{75}^{o}}\]
  done clear
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