Physics-
General
Easy

Question

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

  1. square root of 1 plus 4 x to the power of 2 end exponent end root    
  2. square root of 1 plus 2 x to the power of 2 end exponent end root    
  3. square root of 1 plus x to the power of 2 end exponent end root    
  4. square root of 1 plus 8 x to the power of 2 end exponent end root    

The correct answer is: square root of 1 plus 2 x to the power of 2 end exponent end root

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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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 :

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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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

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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 :

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 f equals R minus fraction numerator K over denominator 2 end fraction s e c invisible function application theta 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 :

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Most materials have the refractive index, n > 1 So, when a light ray from air enters a naturally occurring material, then by Snell’s text law,  end text fraction numerator sin invisible function application theta subscript 1 end subscript over denominator sin invisible function application theta subscript 2 end subscript end fraction equals fraction numerator n subscript 1 end subscript over denominator n subscript 2 end subscript end fraction comma it is understood that the refracted ray bends towards the normal But it never emerges on the same side of the normal as the incident ray According to electromagnetism, the refractive index of the medium is given by the relation, n equals open parentheses fraction numerator c over denominator V end fraction close parentheses equals plus-or-minus square root of epsilon subscript r end subscript mu subscript r end subscript end root, where c is the speed of the electromagnetic waves in vacuum, v its speed in the medium, er and mr are negative, one must choose the negative root of n Such negative refractive index materials can now be artificially prepared and are called metamaterials They exhibit signficantly different optical behaviour, without violating any physical laws Since n is negative, it results in a change in the direction of propagation of the refracted light However, similar to normal materials, the frequency of light remains unchanged upon refraction even in metamaterials For light incident from air on a meta-material, the appropriate ray diagrams

Most materials have the refractive index, n > 1 So, when a light ray from air enters a naturally occurring material, then by Snell’s text law,  end text fraction numerator sin invisible function application theta subscript 1 end subscript over denominator sin invisible function application theta subscript 2 end subscript end fraction equals fraction numerator n subscript 1 end subscript over denominator n subscript 2 end subscript end fraction comma it is understood that the refracted ray bends towards the normal But it never emerges on the same side of the normal as the incident ray According to electromagnetism, the refractive index of the medium is given by the relation, n equals open parentheses fraction numerator c over denominator V end fraction close parentheses equals plus-or-minus square root of epsilon subscript r end subscript mu subscript r end subscript end root, where c is the speed of the electromagnetic waves in vacuum, v its speed in the medium, er and mr are negative, one must choose the negative root of n Such negative refractive index materials can now be artificially prepared and are called metamaterials They exhibit signficantly different optical behaviour, without violating any physical laws Since n is negative, it results in a change in the direction of propagation of the refracted light However, similar to normal materials, the frequency of light remains unchanged upon refraction even in metamaterials For light incident from air on a meta-material, the appropriate ray diagrams

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