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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

- 180°
- 90°
- Can’t be determined
- none of these

#### The correct answer is: 180°

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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 f_{p} and f_{m} 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 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 f_{p} and f_{m} 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 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, , where c is the speed of the electromagnetic waves in vacuum, v its speed in the medium, e_{r} and m_{r} 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 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, , where c is the speed of the electromagnetic waves in vacuum, v its speed in the medium, e_{r} and m_{r} 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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#### The element in the first row and third column of the inverse of the matrix is

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Þ . Hence, element .

.

Hence,

Þ . Hence, element .

#### The element in the first row and third column of the inverse of the matrix is

maths-General

Let Þ |A| = 1

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Hence,

Þ . Hence, element .

.

Hence,

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.

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#### In the above sequence* X* can be

attacks only carbonyl group and reduce it into alcohol group. They do not attack on double bond.

#### In the above sequence* X* can be

chemistry-General

attacks only carbonyl group and reduce it into alcohol group. They do not attack on double bond.

physics-

#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 The coordinates (x1, y(A) of the point P where the ray intersects the upper surface of the slabair boundary are

#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 The coordinates (x1, y(A) of the point P where the ray intersects the upper surface of the slabair boundary are

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#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 Equation for the trajectory y(x) of the ray in the medium is

#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 Equation for the trajectory y(x) of the ray in the medium is

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#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 The incident angle at B(x, y) in the medium and the slope at B are related by the formula

#### A ray of light traveling in air is incident at grazing angle (Ð >i 90º) on a long rectangular slab of a transparent medium of thickness t = 1.0 m The point of incidence is the medium A (0, 0) The medium has a variable index of refraction n(y) given by where The refractive index of air is 1 The incident angle at B(x, y) in the medium and the slope at B are related by the formula

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#### A point object ‘O’ is placed along x-axis An equi-convex thin lens of focal length f=20cm in air is placed so that its principal axis is along x-axis Now the lens is cut at the middle (along the principal axis) and upper half is shifted along x-axis and y-axis by 20cm and 2mm respectively and right side of lower half is filled with water co-ordinates of image formed by lenses are

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