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 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 The incident angle at B(x, y) in the medium and the slope at B are related by the formula

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

An object is placed 20 cm in front of a plano– convex lens of focal length 15 cm The plane surface of the lens is silvered The image will be formed at a distance

Two thin convex lenses of focal lengths f₁ and f₂ are separated by a horizontal distance d and their centers are displaced by a vertical separation D as shown in the figure : Taking the origin of coordinates, O, at the center of the first lens, the x and y-coordinates of the focal point of this lens system, for a parallel beam of rays coming from the left, are given by :

For a convex lens, if real image is formed the graph between (u + v) andu or v is as follows

A ray OP of monochromatic light is incident on the face AB of prism ABCD near vertex B at an incident angle of 60⁰ (see figure) If the refractive index of the material of the prism is , which of the following is (are) correct?

Man and mouse cells are treated with red rhodamine and Green fluorescent dyes separately and then are made to fuse. The resultant cells when kept at 37ºC, the distribution of dye on the surface of cell will be like–

Which of the following statements is not correct?

If then adj A

Which of the following is not true

Which one of the following statements is true

The inverse of is

The inverse of matrix is

A real number multiplicative inverse is the number that, when multiplied by the original number, produces 1 (the identity). Because a× 1/a= 1 is the multiplicative inverse of a. When the inverse of a matrix is multiplied by a given matrix, it produces a multiplicative identity. For example, the inverse of a matrix A is A-1 and A.A-1=A-1.A=I, where I is the identity matrix.
A square matrix with one on the diagonal and zeros everywhere else is known as an identity matrix. Think of the identity matrix as the matrix's prime number.
An invertible matrix is one for which it is possible to calculate the inverse matrix and for which the determinant is not zero.