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question_answer1) An opaque cylindrical tank with an open top has a diameter of 3.00 m and is completely filled with water. When the setting sun reaches an angle of \[37{}^\circ \]above the horizon, sunlight ceases to illuminate any part of the bottom of the tank. How deep is tank in meter?
question_answer2) A cylindrical bucket of depth 60 cm is partly filled with a liquid of refractive index 1.5 and with oil (on top of liquid) of refractive index 2. It appears that the volume of air, volume of liquid and volume of oil are equal, to an observer who views from top of the bucket. The apparent depth of the bucket as seen by the observer given as \[\alpha \]cm. Fill \[\left( \frac{\alpha }{5} \right)\]in OMR, sheet.
question_answer3) An air bubble in glass slab \[\left( \mu =1.5 \right)\]when viewed from one side appears to be at 6 cm and from opposite side 4 cm. Find the thickness (in cm) of glass slab.
question_answer4) A ray \[{{R}_{1}}\]is incident on the plane surface of the glass slab (kept in air) of refractive index \[\sqrt{2}\]at an angle of incidence equal to the critical angle for this air glass system. The refracted ray \[{{R}_{2}}\]undergoes partial reflection and refraction at the other surface. The angle (in degree) between reflected ray \[{{R}_{3}}\]and the refracted ray \[{{R}_{4}}\]at that surface is?
question_answer5) A layer of benzene \[\left( {{\mu }_{1}}=1.5 \right)\]6 cm deep floats on water \[\left( {{\mu }_{2}}=1.33 \right)\] 4 cm deep. When viewed vertically through air the apparent distance (in cm) of the bottom of the vessel below the surface of the benzene will be?
question_answer6) A parallel sided block of glass of refractive index 1.5 which is 36 mm thick rests on the floor of a tank which is filled with water (refractive index = 4/3). The difference apparent depth (in mm) of floor at A & B when seen from vertically above is equal to?
question_answer7) When the surface of the lake is calm, a fish, submerged in water will see the entire outside world within an inverted cone whose apex is situated at the eye of the fish and what angle (in degree) cone subtends at eye of fish : \[\left( \mu w=4/3 \right)\]
question_answer8) The image of the point P as seen by the eye in the figure above P at \[0.11\times xcm\] then the value of x is?
question_answer9) Two optical media have a plane boundary between them. Suppose \[{{\theta }_{icr}}\]is the critical angle of incidence of a beam and \[{{\theta }_{1}}\]is the angle of incidence at which the refracted beam is perpendicular to the reflected one (the beam is assumed to come from an optically denser medium). The relative refractive index of these media if \[\sin {{\theta }_{icr}}/sin{{\theta }_{1}}=\eta =1.28\]is\[0.25\times a\], then value of a is?
question_answer10) A ray of light travelling in air is incident at angle \[\theta =30{}^\circ \]on a long rectangular slab of a transparent medium. The point of incidence is origin O of the co-ordinate system shown in figure. The medium has a variable index of refraction \[\mu \left( y \right)\]given by \[\mu ={{\left( 0.25+k{{y}^{-2}} \right)}^{1/2}}\] where\[k=1.0{{m}^{2}}\]. Equation for trajectory of the ray in the medium is\[{{y}^{2}}=ax\]. The value of a is?
question_answer11) ABCD is the plane of glass cube. A horizontal beam of light enters the face AB at the grazing incidence. Show that the angle \[\theta \]which any ray emerging from BC would make with the normal to BC is given by \[\sin \theta =\cot \alpha \] where \[\alpha \]is the critical angle. The greatest value that the refractive index of glass may have if any of the light is to emerge from BC is\[\sqrt{a}\], then value of a is?
question_answer12) A slab of glass of thickness 5 cm and refractive index 1.5 is held a few centimeter in front of a concave mirror of radius of curvature 40 cm. The faces of the slab being perpendicular to the principal axis of the mirror. How far (in cm) from the mirror must a small object be placed if its image coincides with the object? [consider all events].
question_answer13) A portion of straight glass rod of diameter 4 cm and refractive index \[\mu =2\]is bent into an arc of circle and a parallel beam of light is incident on it as shown in the figure. Find the smallest value of R, in cm (the radius of outer arc) which permits all the light to pass around the arc.
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