A light ray is incident perpendicular to one face of a\[90{}^\circ \]prism and is totally internally reflected at the glass-air interface. If the angle of reflection is\[45{}^\circ ,\] we conclude that the refractive index\[n\]is [AIEEE 2004]
question_answer8) A plano-convex lens of refractive index 1.5 and radius of curvature 30 cm is silvered at the curved surface. Now, this lens has been used to from the image of an object. At what distance from this lens, an object be placed in order to have a real image of the size of the object? [AIEEE 2004]
question_answer9) The angle of incidence at which reflected light is totally polarized for reflection from air to glass (refractive index\[n\]), is [AIEEE 2004]
question_answer10) A fish looking up through the water sees the outside world, contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the water surface, the radius of this circle (in cm) is [AIEEE 2005]
question_answer11) Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm] [AIEEE 2005]
question_answer12) A thin glass (refractive index 1.5) lens has optical power of - 5 D in air. Its optical power in a liquid medium with refractive index 1.6 will be [AIEEE 2005]
question_answer13) The refractive index of glass is 1.520 for red light and 1.525 for bin l light. Let\[{{D}_{1}}\]and\[{{D}_{2}}\]be angles of mmimum deviation for red and blue light respectively in a prism of this glass. Then, [AIEEE 2006]
A)
\[{{D}_{1}}<{{D}_{2}}\]
doneclear
B)
\[{{D}_{1}}={{D}_{2}}\]
doneclear
C)
\[{{D}_{1}}\]can be less than or greater than\[{{D}_{2}}\] depending upon. The angle of prism
question_answer14) If the ratio of the concentration of electrons to that of holes in a semiconductor is\[\frac{7}{5}\]and the ratio of currents is \[\frac{7}{4}\], then what is the ratio of their drift velocities? [AIEEE 2006]
question_answer16) A student measures the focal length of a convex lens by putting an object pin at a distance u from the lens and measuring the distance v of the image pin. The graph between u and v plotted by the student should look like [AIEEE 2008]
question_answer17) An experiment is performed to find the refractive index of glass using a travelling microscope. In this experiment distances are measured by [AIEEE 2008]
question_answer18) In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of\[45{}^\text{o}\]with the x-axis meets the experimental curve at P. The coordinates of P will be [AIEEE 2009]
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: [AIEEE 2009]
An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\]where\[{{\mu }_{0}}\]and\[{{\mu }_{2}}\]are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.
The speed of light in the medium is - [AIEEE 2010]
An initially parallel cylindrical beam travels in a medium of refractive index \[\mu (I)={{\mu }_{0}}+{{\mu }_{2}}I,\]where\[{{\mu }_{0}}\]and\[{{\mu }_{2}}\]are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.
As the beam enters the medium, it will - [AIEEE 2010]
A)
travel as a cylindrical beam
doneclear
B)
diverge
doneclear
C)
converge
doneclear
D)
diverge near the axis and converge near the periphery
Direction: The question has a paragraph followed by two statements, Statement-1 and Statement-2. Of the given four alternatives after the statements, choose the one that describes the statements.
A thin air film is formed by putting the convex surface of a plane-convex lens over a plane glass plate. With monochromatic light, this film gives an interference pattern due to light reflected from the top (convex) surface and the bottom (glass plate) surface of the film.
A nucleus of mass\[M+\Delta m\]is at rest and decays into two daughter nuclei of equal mass \[\frac{M}{2}\]each. Speed of light is c.
Statement-1: When light reflects from the air-glass plate interface, the reflected wave suffers a phase change of \[\pi \].
Statement-2: The centre of the interference pattern is dark. [AIEEE 2011]
A)
Statement-1 is false, Statement-2 is true
doneclear
B)
Statement-1 is true, Statement-2 is false
doneclear
C)
Statement-1 is true, Statement-2 is true and Statement-2 is the correct explanation of Statement-1
doneclear
D)
Statement-1 is true, Statement-2 is true and Statement-2 is not the correct explanation of Statement-1
question_answer23) A car is fitted with a convex side-view mirror of focal length 20 cm. A second car \[2.5\] m behind the first car is overtaking the first car at a relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is [AIEEE 2011]
question_answer24) Let the \[x-z\] plane be the boundary between two transparent media. Medium 1 in \[z\ge 0\] has a refractive index of 2 and medium 2 with \[z>0\] has a refractive index of 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 [AIEEE 2011]
question_answer25) A beaker contains water up to a height \[{{h}_{1}}\]and kerosene of height \[{{h}_{2}}\] above water so that the total height of (water + kerosene) is \[({{h}_{1}}+{{h}_{2}}).\]Refractive index of water is \[{{\mu }_{1}}\] and that of kerosene is \[{{\mu }_{2}}.\] The apparent shift in the position of the bottom of the beaker when viewed from above is: [AIEEE 11-05-2011]
A beam of light consisting of red, green and blue colours is incident on a right-angled prism on face AB. The refractive indices of the material for the above red, green and blue colours are 1.39, 1.44 and 1.47 respectively. A person looking on surface A C of the prism will see [JEE ONLINE 26-05-2012]
question_answer29) A telescope of aperture \[3\times {{10}^{-2}}m\] diameter is focused on a window at 80 m distance fitted with a wire mesh of spacing \[2\times {{10}^{-3}}m\]. Given: \[\lambda =5.5\times {{10}^{-7}}m,\]which of the following is true for observing the mesh through the telescope? [JEE ONLINE 26-05-2012]
A)
Yes, it is possible with the same aperture size.
doneclear
B)
Possible also with an aperture half the present diameter.
question_answer30) Diameter of a plano - convex lens is 6 cm and thickness at the centre is 3 mm. If speed of light in material of lens is\[2\times {{10}^{8}}m/s,\] the focal length of the lens is: [JEE MAIN 2013]
question_answer31) The graph between angle of deviation \[(\delta )\] and angle of incidence (i) for a triangular prism is represented by: [JEE MAIN 2013]
question_answer32) Light is incident from a medium into air at two possible angles of incidence \[{{20}^{0}}\] and \[{{40}^{0}}\] In the medium light travels 3.0 cm in 0.2ns. The ray will: [JEE ONLINE 09-04-2013]
A)
suffer total internal reflection in both cases [a] and [b]
doneclear
B)
suffer total internal reflection in cases [b] only
doneclear
C)
have partial reflection and partial transmission in case [b]
question_answer33) The focal length of the objective and the eyepiece of a telescope are 50 cm and 5 cm respectively. If the telescope is focused for distinct vision on a scale distant 2m from its objective, then its magnifying power will be: [JEE ONLINE 22-04-2013]
question_answer34) The image of an illuminated square is obtained on screen with the help of a converging lens. The distance of the square of the square from the lens is 40 cm. The area of the image is 9 times that of the square. The focal length of the lens is: [JEE ONLINE 22-04-2013]
A light ray falls on square glass slab as shown in the diagram. The index of refraction of the glass, if total internal reflection is to occur at the vertical face, is equal to: [JEE ONLINE 23-04-2013]
question_answer38) A printed page is pressed by a glass of water. The refractive index of the glass and water is 1.5 and 1.33, respectively. If the thickness of the bottom of glass is 1 cm and depth of depth of water is 5 cm, how much the page will appear to be shifted if viewed from the top? [JEE ONLINE 25-04-2013]
question_answer39) A thin convex lens made from crown glass\[\left[ \mu =\frac{3}{2} \right]\] has focal length\[f\]. When it is measured in two different liquids having refractive indices \[\frac{4}{3}\] and \[\frac{5}{3},\] it has the focal lengths \[{{f}_{1}}\] and \[{{f}_{2}}\] respectively. The correct relation between the focal lengths is: [JEE MAIN 2014]
A)
\[{{f}_{2}}>f\] and \[{{f}_{1}}\] becomes negative
doneclear
B)
\[{{f}_{1}}\]and \[{{f}_{2}}\] both become negative
question_answer40) A green light is incident from the water to the air - water interface at the critical angle (θ). Select the correct statement. [JEE MAIN 2014]
A)
The spectrum of visible light whose frequency is more than that of green light will come out to the air medium.
doneclear
B)
The entire spectrum of visible light will come out of the water at various angles to the normal.
doneclear
C)
The entire spectrum of visible light will come out of the water at an angle of 90° to the normal.
doneclear
D)
The spectrum of visible light whose frequency is less than that of green light will come out to the air medium.
question_answer41) A diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is\[\frac{4}{3},\] and the divers eyes are 15 cm below the surface of water. Then the radius of the circle is: [JEE ONLINE 09-04-2014]
The focal lengths of objective lens and eye lens of a Galilean telescope are respectively 30 cm and 3.0 cm. telescope produces virtual erect image of an object situated far away from it at least distance of distinct vision from the eye lens.
In this condition the magnifying power of the Galilean telescope should be:[JEE ONLINE 09-04-2014]
An object is located in a fixed position in front of a screen.
Sharp image is obtained on the screen for two positions of a thin lens separated by 10 cm. The size of the images in two situations are in the ratio 3 : 3. What is the distance between the screen and the object? [JEE ONLINE 11-04-2014]
question_answer44) In a compound microscope the focal length of objective lens is 1.2 cm and focal length of eye piece is 3.0 cm. When object is kept at 1.25 cm in front of objective, final image is formed at infinity. Magnifying power of the compound microscope should be: [JEE ONLINE 11-04-2014]
question_answer45) The refractive index of the material of a concave lens is m. It is immersed in a medium of refractive index \[{{\mu }_{1}}.\] A parallel beam of light is incident on the lens. The path of the emergent rays when \[{{\mu }_{1}}>\mu \] is: [JEE ONLINE 12-04-2014]
question_answer46) The diameter of the objective lens of microscope makes an angle \[\beta \] at the focus of the microscope. Further, the medium between the object and the lens is an oil of refractive index n. Then the resolving power of the microscop [JEE ONLINE 19-04-2014]
A)
increases with decreasing value of n
doneclear
B)
increases with decreasing value of \[\beta \]
doneclear
C)
increases with increasing value of \[n\sin \beta \]
doneclear
D)
increases with increasing value of\[\frac{1}{n\sin 2\beta }\]
question_answer47) Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is [JEE MAIN 2015]
Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is \[\mu ,\] a ray, incident at an angle \[\theta ,\] on the face AB would get transmitted through the face AC of the prism provided. [JEE MAIN 2015]
question_answer49) A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is \[\theta \], then\[\theta \], is close to: [JEE ONLINE 10-04-2015]
question_answer50) You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm- The radius of curvature of the mirror would then be: [JEE ONLINE 10-04-2015]
A thin convex lens of focal length T is put on a plane mirror as shown in the figure.
When an object is kept at a distance 'a' from the lens - mirror combination, its image is formed at a distance\[\frac{a}{3}\]in front of the combination. The value of 'a' is: [JEE MAIN 11-04-2015]
question_answer52) An observer looks at a distant tree of height 10 m with a telescope of magnifying power of 20. To the observer the tree appears: [JEE MAIN - I 3-4-2016]
question_answer53) In an experiment for determination of refractive index of glass of a prism by \[i-\delta ,\] plot, it was found that a ray incident at angle 35°, suffers a deviation of 40° and that it emerges at angle 79°. In that case which of the following is closest to the maximum possible value of the refractive index? [JEE MAIN - I 3-4-2016]
A convex lens, of focal length 30cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of: [JEE ONLINE 09-04-2016]
question_answer56) To determine refractive index of glass slab using a travelling microscope, minimum number of readings required are: [JEE ONLINE 10-04-2016]
A hemispherical glass body of radius 10cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen: [JEE ONLINE 10-04-2016]
question_answer58) Two stars are 10 light years away from the earth. They are seen through a telescope of objective diameter 30cm. The wavelength of light 600 nm. To see the stars just resolved by the telescope, the minimum distance between them should be (1 light year \[=9.46\times {{10}^{15}}\]m) of the order of: [JEE ONLINE 10-04-2016]
question_answer59) A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is: [JEE Main 2017]
A)
real and at a distance of 40 cm from the divergent lens
doneclear
B)
real and at a distance of 6 cm from the convergent lens
doneclear
C)
real and at a distance of 40 cm from convergent lens
doneclear
D)
virtual and at a distance of 40 cm from convergent lens.
question_answer60) In an experiment a convex lens of focal length 15 cm is placed coaxially on an optical bench in front of a convex mirror at a distance of 5 cm from it. It is found that an object and its image coincide, if the object is placed at a distance of 20 cm from the lens. The focal length of the convex mirror is - [JEE Online 09-04-2017]
A plan convex lens becomes an optical system of \[28cm\] focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length\[10cm\]. The refractive index of the material of lens if: [JEE Online 15-04-2018]
A particle is oscillating on the X-axis with an amplitude \[2cm\] about the point \[{{x}_{0}}=10cm\] with a frequency\[\omega \]. A concave mirror of focal length \[5cm\] is placed at the origin (see figure)
Identify the correct statements: [JEE Online 15-04-2018]
[A] The image executes periodic motion
[B] The image executes no n-periodic motion
[C] The turning points of the image are asymmetric w.r.t the image of the point at \[x=10cm\]
[D] The distance between the turning points of the oscillation of the image is\[\frac{100}{21}\]
question_answer63) A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of\[10cm\]. The separation between the two lenses is\[2cm\]. The focal lengths of the component lenses [JEE Online 15-04-2018 (II)]
question_answer64) A ray of light is incident at an angle of \[{{60}^{o}}\]on one face of a prism of angle\[{{30}^{o}}.\]The emergent ray of light makes an angle of with incident ray. The angle made by the emergent ray with second face of prism will be: [JEE Main Online 16-4-2018]
question_answer65) A convex lens is put 10 cm from a light source and it makes a sharp image on a screen, kept 10 cm from the lens. Now a glass block (refractive index 1.5) of 1.5 cm thickness is placed in contact with the light source. To get the sharp image again, the screen is shifted by a distance d. Then d is: [JEE Main 09-Jan-2019 Morning]
Consider a tank made of glass (refractive index 1.5) with s. thick bottom. It is filled with a liquid of refractive index \[\mu \]. A student finds that, irrespective of what the incident angle I (see figure) is for a beam of light entering the liquid, the light reflected from the liquid glass interface is never completely polarized. For this to happen, the minimum value of \[\mu \] is: [JEE Main 09-Jan-2019 Morning]
question_answer67) Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror \[\left( {{M}_{1}} \right)\] and parallel to the second mirror \[({{M}_{2}})\] is finally reflected from the second mirror \[({{M}_{2}})\] parallel to the first mirror\[\left( {{M}_{1}} \right)\]. The angle between the two mirrors will be: [JEE Main 09-Jan-2019 Evening]
question_answer68) A plano convex lens of refractive index \[{{\mu }_{1}}\] and focal, length \[{{f}_{1}}\] is kept in contact with another piano concave lens of refractive index \[{{\mu }_{2}}\]and focal length\[{{f}_{2}}\]. If the radius of curvature of their spherical faces is R each and \[{{f}_{1}}\,=\,2{{f}_{2}}\], then \[{{\mu }_{1}}\,and\,\,{{\mu }_{2}}\] are related as- [JEE Main 10-Jan-2019 Morning]
question_answer69) The eye can be regarded as a single refracting surface. The radius of curvature of this surface is equal to that of cornea (7.8 mm). This surface separateds two media of refractive indices 1 and 1.34. Calculate the distance from the refracting surface at which a parallel beam of light will come to focus- [JEE Main 10-Jan-2019 Evening]
The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if \[{{D}_{m}}\] is the angle of minimum deviation? [JEE Main 11-Jan-2019 Morning]
question_answer71) An object is at a distance of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction of the image will be- [JEE Main 11-Jan-2019 Morning]
question_answer72) In a double -slit experiment, green light (\[5303\text{ }{\AA}\]) falls on a double slit having a separation of 19.44\[\mu m\] and a width of 4.05\[\mu m\]. The number of bright fringes between the first and the second diffraction minima is- [JEE Main 11-Jan-2019 Evening]
question_answer73) A monochromatic light is incident at a certain angle on an equilateral triangular prism and suffers minimum deviation. If the refractive index of the material of the prism is \[\sqrt{3},\]then the angle of incidence is- [JEE Main 11-Jan-2019 Evening]
A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2L as shown below The distance over which the man can see the image of the light source in the mirror is- [JEE Main 12-Jan-2019 Morning]
question_answer76) A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is \[30V\,{{m}^{-1}},\]then the amplitude of the electric field for the wave propagating in the glass medium will be- [JEE Main 12-Jan-2019 Morning]
question_answer78) A plano-convex lens (focal lengthy\[{{f}_{2}}\], refractive index \[{{\mu }_{2}},\]radius of curvature R) fits exactly into a plano-concave lens (focal length \[{{f}_{1}},\]refractive index \[{{\mu }_{1}},\]radius of curvature -R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be- [JEE Main 12-Jan-2019 Evening]
question_answer79) An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of the lens. The position and size of the final image will be: [JEE Main 8-4-2019 Morning]
A)
40 cm from the convergent mirror, same size as the object
doneclear
B)
20 cm from the convergent mirror, same size as the object
doneclear
C)
20 cm from the convergent mirror, twice the size of the object
doneclear
D)
40 cm from the convergent lens, twice the size of the object
In figure, the optical fiber is \[\ell =2m\]long and has a diameter of \[d=20\mu m\]. If a ray of light is incident on one end of the fiber at angle \[{{\theta }_{1}}={{40}^{o}},\]the number of reflection it makes before emerging from the other end is close to: (refractive index of fibre is 1.31 and sin \[40{}^\circ \text{ }=\text{ }0.64\]) [JEE Main 8-4-2019 Morning]
question_answer81) Calculate the limit of resolution of a telescope objective having a diameter of 200 cm, if it has to detect light of wavelength 500 nm coming from a star:- [JEE Main 8-4-2019 Afternoon]
question_answer82) A convex lens (of focal length 20 cm) and a concave mirror, having their principal axes along the same lines, are kept 80 cm apart from each other. The concave mirror is to the right of the convex lens. When an object is kept at a distance of 30 cm to the left of the convex lens, its image remains at the same position even if the concave mirror is removed. The maximum distance of the object for which this concave mirror, by itself would produce a virtual image would be : [JEE Main 8-4-2019 Afternoon]
The figure shows a Young's double slit experimental setup. It is observed that when a thin transparent sheet of thickness t and refractive index μ is put in front of one of the slits, the central maximum gest shifted by a distance equal to n fringe widths. If the wavelength of light used is \[\lambda ,t\]will be : [JEE Main 9-4-2019 Morning]
question_answer84) A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is : [JEE Main 9-4-2019 Morning]
A thin convex lens L (refractive index = 1.5) is placed on a plane mirror M. When a pin is
placed at A, such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index \[{{\mu }_{1}}\] is put between the lens and the mirror, The pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of μ1 will be :- [JEE Main 9-4-2019 Afternoon]
question_answer86) A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances \[{{x}_{1}}\] and \[{{x}_{2}}\] \[({{x}_{1}}>{{x}_{2}})\]from the lens. The ratio of \[{{x}_{1}}\] and \[{{x}_{2}}\] is: [JEE Main 9-4-2019 Afternoon]
question_answer87) Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600nm. coming from a distant object, the limit of resolution of the telescope is close to :- [JEE Main 9-4-2019 Afternoon]
One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is \[{{\mu }_{1}}\]and that of 2 is \[{{\mu }_{2}}\], then the focal length of the combination is : [JEE Main 10-4-2019 Morning]
A ray of light AO in vacuum is incident on a glass slab at angle \[60{}^\circ \] and refracted at angle \[30{}^\circ \] along OB as shown in the figure. The optical path length of light ray from A to B is: [JEE Main 10-4-2019 Morning]
The graph shows how the magnification m produced by a thin lens varies with image distance v. What is the focal length of the lens used? [JEE Main 10-4-2019 Afternoon]
question_answer91) The value of numerical aperature of the objective lens of a microscope is 1.25. If light of wavelength \[5000\text{ }{\AA}\] is used, the minimum separation between two points, to be seen as distinct, will be : [JEE Main Held on 12-4-2019 Morning]
A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). If a small particle is floating on the surface of water, its image as seen, from directly above the glass, is at a distance d from the surface of water. The value of d is close to : (Refractive index of water = 1.33)
question_answer93) In a double slit experiment, when a thin film of thickness t having refractive index m is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of t is (\[\lambda \]is the wavelength of the light used) : [JEE Main Held on 12-4-2019 Morning]
A transparent cube of side d, made of a material of refractive index \[{{\mu }_{2}},\]is immersed in a liquid of refractive index \[{{\mu }_{1}}({{\mu }_{1}}<{{\mu }_{2}}).\]A ray is incident on the face AB at an angle \[\theta \](shown in the figure). Total internal reflection takes place at point E on the face BC.
The \[\theta \] must satisfy : [JEE Main 12-4-2019 Afternoon]
question_answer95) A system of three polarizers \[{{P}_{1}},{{P}_{2}},{{P}_{3}}\]is set up such that the pass axis of\[{{P}_{3}}\]is crossed with respect to that of \[{{P}_{1}}\]. The pass axis of \[{{P}_{2}}\]is inclined at \[60{}^\text{o}\] to the pass axis of \[{{P}_{3}}\]. When a beam of unpolarized light of intensity \[{{I}_{0}}\] is incident on \[{{P}_{1}},\]the intensity of light transmitted by the three polarizers is I. The ratio \[({{I}_{0}}/I)\] equals (nearly) : [JEE Main 12-4-2019 Afternoon]
question_answer96) If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to [JEE MAIN Held on 07-01-2020 Morning]
question_answer97) A thin lens made of glass (refractive index = 1.5) of focal length f = 16 cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is \[{{f}_{l}}\], then the ratio \[\frac{{{f}_{l}}}{f}\]is closest to the integer [JEE MAIN Held on 07-01-2020 Evening]
question_answer98) The magnifying power of a telescope with tube length 60 cm is 5. What is the focal length of its eye piece? [JEE MAIN Held On 08-01-2020 Morning]
question_answer99) A point object in air is in front of the curved surface of a Plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, Then the focal length of the lens (in cm) is ______. [JEE MAIN Held On 08-01-2020 Morning]
question_answer100) An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematically and are not to scale) [JEE MAIN Held on 08-01-2020 Evening]
question_answer101) The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is\[4\times {{10}^{5}}\text{ }km\]. With light of wavelength of 5500\[\overset{\text{o}}{\mathop{\text{A}}}\,\], the minimum separation between objects on the surface of moon, so that they are just resolved, is close to: [JEE MAIN Held on 09-01-2020 Morning]
question_answer102) A vessel of depth 2h is half filled with a liquid of refractive index \[2\sqrt{2}\] and the upper half with another liquid of refractive index\[\sqrt{2}\]. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be [JEE MAIN Held on 09-01-2020 Morning]
question_answer103) There is a small source of light at some depth below the surface of water (refractive index \[=\frac{4}{3}\]) in a tank of large cross-sectional surface area. Neglecting any reflection from the bottom and absorption by water, percentage of light that emerges out of surface is (nearly) [Use the fact that surface area of a spherical cap of height h and radius of curvature r is\[2\pi rh\]] [JEE MAIN Held on 09-01-2020 Evening]