Physics-
General
Easy
Question
Due to a vertical temperature gradient in the atmosphere, the index of refraction varies Suppose index of refraction varies as
is the index of refraction at the surface and a
A person of height h = 2.0 m stands on a level surface Beyond what distance will he not see the runway?
![](data:image/png;base64,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)
- 2000 m
- 3000 m
- 2500 m
- 3500 m
The correct answer is: 2000 m
Related Questions to study
physics-
Find the variation of refractive index assuming it to be a function of y such that a ray entering origin at grazing incidence follows a parabolic path y = x2 as shown in fig
![](data:image/png;base64,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)
Find the variation of refractive index assuming it to be a function of y such that a ray entering origin at grazing incidence follows a parabolic path y = x2 as shown in fig
![](data:image/png;base64,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)
physics-General
chemistry-
Metal oxides which decomposes on heating is
Metal oxides which decomposes on heating is
chemistry-General
chemistry-
One mole of an organic compound A with the formula
reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. The compound A is
One mole of an organic compound A with the formula
reacts completely with two moles of HI to form X and Y. When Y is boiled with aqueous alkali it forms Z. Z answers the iodoform test. The compound A is
chemistry-General
physics-
A reflecting surface is represented by the equation
A ray travelling in negative x-direction is directed towards positive y-direction after reflection from the surface at point P Then co-ordinates of point P are
![](data:image/png;base64,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)
A reflecting surface is represented by the equation
A ray travelling in negative x-direction is directed towards positive y-direction after reflection from the surface at point P Then co-ordinates of point P are
![](data:image/png;base64,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)
physics-General
physics-
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of bird relative to the fish looking upward in cm/s is
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)
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of bird relative to the fish looking upward in cm/s is
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)
physics-General
physics-
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of fish formed after reflection in the mirror as seen by the bird in cm/s
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)
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of fish formed after reflection in the mirror as seen by the bird in cm/s
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)
physics-General
maths-
Consider the system of equations ax+by =0 , cx +dy=0 where a, b, c, d
{0,1}
Statement ‐ I The probability that the system of equations has a unique solution is 3/8 Statement ‐ II The probability that the system has a solution is 1.
Consider the system of equations ax+by =0 , cx +dy=0 where a, b, c, d
{0,1}
Statement ‐ I The probability that the system of equations has a unique solution is 3/8 Statement ‐ II The probability that the system has a solution is 1.
maths-General
chemistry-
Which alcohol cannot be oxidized by ![M n O subscript 2 ?](data:image/png;base64,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)
Which alcohol cannot be oxidized by ![M n O subscript 2 ?](data:image/png;base64,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)
chemistry-General
physics-
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of fish as seen by the bird directly in cm/s is
![](data:image/png;base64,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)
A bird in air is diving vertically over a tank with speed 5cm/s Base of the tank is silvered A fish in the tank is rising upward along the same line with speed 2cm/s Water level is falling at a rate of 2cm/s
Speed of the image of fish as seen by the bird directly in cm/s is
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)
physics-General
physics-
A Ray of light goes from A in a medium where the speed of light is V1 to a point B in a medium where the speed of light is V2 as shown in figure The path of the rays as shown in figure Answer the following questions,based on the above paragraph The slope of
curve is
![](data:image/png;base64,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)
A Ray of light goes from A in a medium where the speed of light is V1 to a point B in a medium where the speed of light is V2 as shown in figure The path of the rays as shown in figure Answer the following questions,based on the above paragraph The slope of
curve is
![](data:image/png;base64,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)
physics-General
physics-
A Ray of light goes from A in a medium where the speed of light is V1 to a point B in a medium where the speed of light is V2 as shown in figure The path of the rays as shown in figure Answer the following questions,based on the above paragraph The time taken for the light to go from the point A to the point B in the figure
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)
A Ray of light goes from A in a medium where the speed of light is V1 to a point B in a medium where the speed of light is V2 as shown in figure The path of the rays as shown in figure Answer the following questions,based on the above paragraph The time taken for the light to go from the point A to the point B in the figure
![](data:image/png;base64,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)
physics-General
physics-
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point Which of the following statements are correct regarding spherical aberration :
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)
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point Which of the following statements are correct regarding spherical aberration :
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)
physics-General
physics-
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point For paraxial rays, focal length approximately is
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)
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point For paraxial rays, focal length approximately is
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)
physics-General
physics-
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point The total deviation suffered by the ray falling on mirror at an angle of incidence equal to 60° is
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)
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point The total deviation suffered by the ray falling on mirror at an angle of incidence equal to 60° is
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)
physics-General
physics-
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point If fp and fm represent the focal length of paraxial and marginal rays respectively, then correct relationship is :
![](data:image/png;base64,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)
Spherical aberration in spherical mirrors is a defect which is due to dependence of focal length ‘f’ on angle of incidence ‘ q ’ as shown in figure is given by
where R is radius of curvature of mirror and q is the angle of incidence The rays which are closed to principal axis are called paraxial rays and the rays far away from principal axis are called marginal rays As a result of above dependence different rays are brought to focus at different points and the image of a point object is on a point If fp and fm represent the focal length of paraxial and marginal rays respectively, then correct relationship is :
![](data:image/png;base64,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)
physics-General