Physics-
General
Easy
Question
In the figure ABC is the cross section of a right angled prism and BCDE is the cross section of a glass slab. The value of
so that light incident normally on the face AB does not cross the face BC is (given ![open s i n to the power of negative 1 end exponent invisible function application left parenthesis 3 divided by 5 right parenthesis equals 37 to the power of ring operator end exponent close parentheses](data:image/png;base64,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)
![](data:image/png;base64,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)
The correct answer is: ![theta less or equal than 37 to the power of ring operator end exponent](data:image/png;base64,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)
Related Questions to study
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An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?
An object is placed in front of a convex mirror at a distance of 50 cm. A plane mirror is introduced covering the lower half of the convex mirror. If the distance between the object and the plane mirror is 30 cm, it is found that there is no parallax between the images formed by the two mirrors. What is the radius of curvature of the convex mirror?
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A long rectangular slab of transparent medium of thickness 'd' placed such a table with its length parallel to the x-axis and width parallel to the y-axis. A ray of light travelling in air makes a near normal
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![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556725/1/1047168/Picture119.png)
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A long rectangular slab of transparent medium of thickness 'd' placed such a table with its length parallel to the x-axis and width parallel to the y-axis. A ray of light travelling in air makes a near normal
incidence on the slab as shown. Taking the point of incidence as origin (0,0,0). The refraction index
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![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/556725/1/1047168/Picture119.png)
The
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physics-
A point source S is placed midway between two converging mirrors having equal focal length as shown in figure. Find the values of d for which only one image is formed.
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)
A point source S is placed midway between two converging mirrors having equal focal length as shown in figure. Find the values of d for which only one image is formed.
![](data:image/png;base64,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)
physics-General
physics-
A U-shaped wire is placed before a concave mirror having radius of curvature 20 cm as shown in figure. Find the total length of the image.
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)
A U-shaped wire is placed before a concave mirror having radius of curvature 20 cm as shown in figure. Find the total length of the image.
![](data:image/png;base64,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)
physics-General
physics-
A convex mirror of focal length 10an is shown in the figure. A linear object AB=5 cm is placed along the optic axis. Point
is at a distance of 25 cm from the pole of mirror. The length of image of AB is
![](data:image/png;base64,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)
A convex mirror of focal length 10an is shown in the figure. A linear object AB=5 cm is placed along the optic axis. Point
is at a distance of 25 cm from the pole of mirror. The length of image of AB is
![](data:image/png;base64,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)
physics-General
physics-
A reflecting surface is represented by the equation
A ray travelling horizontally becomes vertical after reflection. The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,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)
A reflecting surface is represented by the equation
A ray travelling horizontally becomes vertical after reflection. The coordinates of the point (s) where this ray is incident is
![](data:image/png;base64,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)
physics-General
physics-
.Two bodies A and B are moving towards a plane mirror with speeds
and
respectively as shown in fig. The speed of image of A respect to the body B is
![](data:image/png;base64,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)
.Two bodies A and B are moving towards a plane mirror with speeds
and
respectively as shown in fig. The speed of image of A respect to the body B is
![](data:image/png;base64,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)
physics-General
physics-
A point object is moving with a speed v before an arrangement of two mirrors as shown in figure. The magnitude of velocity of image in mirror
with respected to image in mirror
is
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)
A point object is moving with a speed v before an arrangement of two mirrors as shown in figure. The magnitude of velocity of image in mirror
with respected to image in mirror
is
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)
physics-General
physics-
A point source of light ' S ' at a distance
from the screen A produces light intensity I0 at the centre of the screen. If a completely reflecting mirror M is placed at a distance
behind the source as shown in the figure, treating object and its image as incoherent with each other, find the intensity at the centre of the screen.
![](data:image/png;base64,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)
A point source of light ' S ' at a distance
from the screen A produces light intensity I0 at the centre of the screen. If a completely reflecting mirror M is placed at a distance
behind the source as shown in the figure, treating object and its image as incoherent with each other, find the intensity at the centre of the screen.
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAANYAAADVCAMAAAAcqf6yAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAL9UExURf////39/eTk5JKSknh4eHl5eXR0dKGhoba2tnZ2doKCgqWlpdfX17GxsZaWlvj4+OLi4nt7ewAAABMTE87Ozu7u7ikpKefn5/T09E1NTSAgIOPj45GRkQwMDNHR0cvLywgICK2trff390dHRxERERYWFt/f3+rq6jMzMxQUFGZmZvb29kxMTGNjYxISEoCAgBsbG3BwcNnZ2SMjIxoaGsrKyvX19UZGRpqammtraycnJ/Dw8JycnDQ0NLCwsBAQEHNzc0JCQqampsjIyA0NDQEBAZOTk5mZmd3d3aCgoI+Pj05OTigoKFBQUDY2NiwsLGlpaZWVlZSUlB4eHujo6KioqAQEBJ2dnZeXl7e3twUFBampqdPT0ysrK319fTIyMj8/P/v7+/r6+jc3N1xcXKSkpCEhIdjY2MDAwKurq7i4uAsLC83NzURERG9vb+vr6yIiIl9fX/Hx8Tg4OFJSUldXV/7+/r6+vg4ODkVFRWdnZyYmJtvb2wICAg8PD7y8vMPDw1tbW9DQ0KqqqhUVFYiIiGJiYjs7O/z8/NLS0kFBQe/v70NDQ4qKim1tbTo6On9/f6+vr/Ly8jw8PB0dHU9PT46Ojtzc3MzMzLu7u4mJiezs7F5eXsLCwvPz8y4uLp6entbW1uHh4YGBgS8vL6Ojo4aGhu3t7fn5+ebm5unp6aKiohgYGBkZGUhISH5+fi0tLYeHhyUlJVpaWsnJyWFhYWxsbJubm5iYmJ+fn9ra2kpKSmVlZWhoaG5ubpCQkODg4ElJSWBgYOXl5XFxcYODg7m5uc/Pz2pqar+/v4WFhVZWVkBAQLS0tFRUVHp6enx8fK6urtXV1Xd3dz4+Pl1dXYSEhD09PcTExLq6utTU1FFRUTk5OXV1dXJycmRkZBwcHFVVVbOzs8bGxjExMcfHx97e3rKysr29vaenpzU1NTAwMFlZWaysrMXFxYyMjI2NjYuLi1hYWLW1tUtLSyQkJMHBwRcXFwMDAyoqKh8fHwkJCQoKClNTUwAAAFXp6IsAAAD/dFJOU///////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////AGb8ilkAAAAJcEhZcwAAFxEAABcRAcom8z8AAAftSURBVHhe7V3RjeMgEE0NSHTAh0Uj0AySe0D0AHVRAZ3cDODsrtbZBDvMejnefayti4Ofh5kHhBnfJiYmJib+W3AXY1T1JCPE6KyuJ91gv7T5fvDImPD1BMBXxiLn9awbkujchEYe9RigGGPdbXXzjIV62AtGMHEnwpfPZ90gGTP1sBeMFMzV45sSkfXuH9BDxPql5/eAUfKDyRqhF3a3VlysYLKe9AFfrBesBiYnuOpvLb2qm2Fr32aMuiW2lDZWCTGju28peHCWbY+yDzjQCoxZPFbAiIDWipF3YUs564QFnpopbSwJI3xvWmrFBsCHe8Z4tBZ2CWjDYrBw3X3L5GDBOwcNtBZ0CdARNBY+xb7WCsxIBMT4jg1la2HX84GhlHSPhClpj4AYf5fLDsjWgqGgXLLw97aWFptLgUP3e4DFWuBSLBuru2/JewCEQXaOv32w5K4AHoye1d1aXNx7nhYdB4a+jt9jibc89Q28rvQJBDzJXubSNq3GIQ8fse8Ft65rUr2GoRq+PqnSyb1cV7HkVt8PmDF+njTm436zyPL1n4+7NbWhfwsZXFM0dG9CffhyT8A8VRiaB5ihPk/9O2JlvackX6C6av4duATUUYW/QbFE0hopLe9M90WTDDprae+StJKmExJZi1snpYLh0li+5SNyAhBGQtqQMWgknNY6jqlbb4BWw+kW9ypJNZhuBdAtp/lgvuVlnQqPFQnvLUzdOgVyWkNayw6rWxStEeqWVhDjR9Mt5OTH0y03des8pm69BcNaS5K0RkpL2zSabgEniPFpLN3yKiYXcLfOSL6lZSy/qQ6mW1sTU7dOgZzWqLpVj/qClBYP962SfUFoLW6jjIPplrYxRasH0y0PupVbmbp1BlO33oKpW6dASmtI3QpuPN0KqFt+ON2SNrcydesMpm69BVO3ToGUFveSpjVKa6FumaF066aDS1H5wXwLdKtsKBxMt7Y8malbFTCUdEpz3paQQk6r0Vo6CWWdSSX/61Vc3Vp8yQlRemnMH6al1axbqu4/xJTvBlBayyvUrTZrpW1b5dcqIk9BRIvj5n4Vmn3L1FzKxkIlZLqVIJrBQatvOcbWknZ4xUioj+qWFoyJ9hTAy+tWgBtkS3POJjmt1lGGTsCrddvD9UcZcA10RGa2bvwaaGnpQ/MtD/GwpmG/CFrdinFptFYOnzmDvW2YQUSLa9wIH3jrOmFNikZeLasFRNbSoFsem2n1rbqdA++z6UIiWpuYtkZCudlobUrMv3oklNWlbFvIuLpuyWVNKgSZywC9jqtbK+RYE+tO39dBS0tHmtYoraVtu24dBRUt3NwfLW8fEx4CnW7hJsl23zoKIlpHdesgrh4Jj4KcVru1uPd1xPsy/oC1rBFCLNuY90XQ0uLtuoVzEkTT46C0FlaXaNatUFk11qCiooWb+6Nq1628kpHRMtal060YcDWi2beWSqqxEhARrTobbI6E/INWy21ePhLi6kxB022S02r0LVVJsaYLL2+tey9sK7JFS4u75vytsqrLUtPyJ6W1dFCgW+27aIKLubZhC6ho5c39brz5Fm7uP+BbB0FEq2zuPxAJj+HykfAgyGlNa50AMa123ToESmthdYkjunUEVLR4iFjpaTDdiqlUKBzLt3zZ3D8j4UmQ05rWOgFiWiPqllcRdIukNSpaHCaD0nk3lm7h5n6c4Y6mW3UpYkbCUyCnNai1SGhN3ToNrC6xjFZNMiiYnAynW7hJEg7G8i2/vTiHKMDPSPgWTGudAjmt4XTrpgPqVj3pCzJaWKEwhrF0i6Nu4TaYweZbqv7ANewIfs63jmPq1lswom7x4Iabb3kbkwxxLN1SETf3j+Zb3uVNkmQBfkbCt+Ana/mmTWh37F12GWvxYI6815RbI/ZSXMlpPQjwWh166bd2Ym8nOa1u+Z906+ArTsxuQjIZLaz0JO0PunWY1u9ZC3VLYpqIfRwy/qC1vKs/cD0IGT4E3k6Laxt+1Vp37AZ4nVI0Zmml5etle8kn5LS+37te8A5kYzGCmxYJzJJ2c2quoFvlJfdwJ23WSrn4jha/GwkLdnTLizX/baxNG2qppAv4llfL92kkMM1/G0NGrF76+7old3UrHaO1FcL6Vd2yMT56jbM5RmvbR/qruoUVkBE7AX6rJ9bmW3xb9r6Ibn27d1friTX7lsgKn66hW9+sFWra435vgifvdrOBbK1OsyvHV9AtEOJFWbmytJ81vdTqcF+BQmyUTYLJncvIaRWP+IIoGFtVWtN+OtM+rRuXcNlizSq//zettR69DlMHGAn73ZsHmH1acJkNcNleD6WzFswhZaqvcebeB/j3Y7s6BPgU3nO2Fsez8HNuf/7S/K1kuoU/cMHd5flWyQt8snSRK4wxXKgwTN9sTpEspQofwgIZoIMfoqHlsQIyAkOGw1JvL9R6K59LwC+UxP6ndQoxjJTPEVmr/sWQUZo2QfsnwOUXgFhZ/sukf3aJ9hBVAQvajS5kIC0ytGX0noNiuf+DtWR6BpnqZwvEK5eYYljjnNsX9z4A3wrF+5+3WjOOcZN55mceKcAHynfvLoh2BQ6eeAkA8knMuMc1iIS6pPY/GzTC8BLQlnn9FpR9GQG7k3kS4JOBDzlwkCzHKneyvVHtBxRekchNBfCf7uxnl/7434ejjL+NB2PCv45prb+EQa2l2mtWT0xMTExMTExMTEzs43b7Bx7fqKbZi76rAAAAAElFTkSuQmCC)
physics-General
physics-
A point source of light S is placed in front of two large mirrors as shown. Which of the following observers will see only one image of S?
![](data:image/png;base64,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)
A point source of light S is placed in front of two large mirrors as shown. Which of the following observers will see only one image of S?
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physics-General
physics-
A two eyed man is looking at the junction of two mutually perpendicular mirrors from a far off distance. Assume no reflection to occur from the edge. Then if both the eyes are open
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BGflfHBUmrUnxP0rxhGqB4SckDrFF2y7YQwmcCXtibki4upLghAytFvmeRAf30AeFhNN1ktYjrSnLrKL3FbeR3GSz7q2RgSuC0hJuBN9h2dGzJopGljtLIVklCgGSwIIDruDQXlLyQIl80Wnabyc3AA0Yqmy2iaUAhwCHJFNH0BEqWI6/U0dzjkORmIHV07c3bkUsyMM10PNbN3bKRn8v/HwGUvDAXiwzonldDH1203Y2/ZDUDI8Xj4TZyJQ3otpEpolP+/xpZMngmaZnBalcycl3LwLC82l+Ph+LZVTZQgbOKC5wPVIpmpERmYNnANTb38EWTAXdQc0/O90gGi3skg4Yr/nsGocCkWCx+3YBjM/g+u++QZf8ADkATgQL9CjgAAAAASUVORK5CYII=)
A two eyed man is looking at the junction of two mutually perpendicular mirrors from a far off distance. Assume no reflection to occur from the edge. Then if both the eyes are open
![](data:image/png;base64,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)
physics-General
physics-
A point source of light ' S ' is placed at a distance 10 cm in front of the center of a mirror of width 20 cm suspended vertically on a wall. A man walks with a speed 10 cm/s in front of the mirror at a distance of 20 cm from it as shown in figure. Find the maximum time during which he can see the image of the source S in the mirror.
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)
A point source of light ' S ' is placed at a distance 10 cm in front of the center of a mirror of width 20 cm suspended vertically on a wall. A man walks with a speed 10 cm/s in front of the mirror at a distance of 20 cm from it as shown in figure. Find the maximum time during which he can see the image of the source S in the mirror.
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)
physics-General
physics-
A particle is moving in a circle in front of a plane mirror in the situation as shown in figure. The plane of motion of the particle is perpendicular to the plane of mirror. Then the motion of image of particle with respected to the particle is
![](data:image/png;base64,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)
A particle is moving in a circle in front of a plane mirror in the situation as shown in figure. The plane of motion of the particle is perpendicular to the plane of mirror. Then the motion of image of particle with respected to the particle is
![](data:image/png;base64,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)
physics-General
physics-
A plane mirror ' M ' and a concave mirror ' X ' are kept at a separation of 40 an with their reflecting faces facing each other as shown in figure. An object AB is kept perpendicular to the principal axis in position (1). Considering successive reflections first at mirror ' X ' and then at ' M', a real image is formed in front of 'M at a normal distance 8 am form it. If the object is moved to new position (2), the real image is formed at 20 cm from ' M ' with the reflections as described earlier.
Keeping the object in position (1), if the plane mirror is replaced with a convex mirror ' Y ' of focal length 20 m facing the mirror ' X ' after successive reflections first at ' X ' and then at ' Y ', the final image will be
![](data:image/png;base64,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)
A plane mirror ' M ' and a concave mirror ' X ' are kept at a separation of 40 an with their reflecting faces facing each other as shown in figure. An object AB is kept perpendicular to the principal axis in position (1). Considering successive reflections first at mirror ' X ' and then at ' M', a real image is formed in front of 'M at a normal distance 8 am form it. If the object is moved to new position (2), the real image is formed at 20 cm from ' M ' with the reflections as described earlier.
Keeping the object in position (1), if the plane mirror is replaced with a convex mirror ' Y ' of focal length 20 m facing the mirror ' X ' after successive reflections first at ' X ' and then at ' Y ', the final image will be
![](data:image/png;base64,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)
physics-General
physics-
In the figure shown consider the first reflection at the plane mirror and second at the convex mirror. AB is object.
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)
In the figure shown consider the first reflection at the plane mirror and second at the convex mirror. AB is object.
![](data:image/png;base64,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)
physics-General