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.

  respectively are

Light is incident normally in face AB of a prism as shown in figure A liquid of refractive index m is placed on face AC of the prism The prism is made of glass of refractive index 3/2 The limits of m for which total internal reflection takes place on face AC is

An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure The beaker height is 3h and its radius h When the beaker is filled with a liquid up to height 2h, he can see the lower end of the rod Then the refractive index of the liquid is

A rectangular glass slab ABCD of refractive index n₁ is immersed in water of refractive index A ray of light is incident a the surface AB of the slab as shown The maximum value of the angle of incidence a_max, such that the ray comes out only from the other surface CD, is given by