Question
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
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)
- 60 cm to the left of the lens
- 60 cm to the right of the lens
- 12 cm to the left of the lens
- 12 cm to the right of the lens
The correct answer is: 12 cm to the left of the lens
Related Questions to study
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 :
![](data:image/png;base64,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)
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 :
![](data:image/png;base64,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)
For a convex lens, if real image is formed the graph between (u + v) andu or v is as follows
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?
![](data:image/png;base64,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)
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?
![](data:image/png;base64,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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–
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?
Which of the following statements is not correct?
If
then adj A
If
then adj A
Which of the following is not true
Which of the following is not true
Which one of the following statements is true
Which one of the following statements is true
The inverse of
is
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.
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.