The focal length of a convex lens is 25 cm at what distance from the optical centre of the lens

1. Spherical Mirrors:

(i) A mirror, which is polished from the outer side of a hollow sphere, such that the reflecting side is towards hollow side, is called a concave mirror.

(ii) A mirror which is polished from the hollow side of the sphere, such that the reflecting surface is towards bulging side, is called a convex mirror.

(iii) The focal length f of a spherical mirror is half of the radius of curvature R. f=R2

(iv) The mirror formula for spherical mirrors is 1v+1u=1f and gives the relationship between object distance u, image distance v and the focal length f.

(v) The magnification produced by a spherical mirror, m=-vu.

2. New Cartesian Sign Conventions:

In this convention, the pole (P) of the mirror is taken as the origin. The principal axis of the mirror is taken as the x-axis of the coordinate system. The conventions are as follows –

(i) The object is always placed to the left of the mirror. This implies that the light from the object falls on the mirror from the left-hand side.

(ii) All distances parallel to the principal axis are measured from the pole of the mirror.

(iii) All the distances measured to the right of the origin (along + x-axis) are taken as positive while those measured to the left of the origin (along - x-axis) are taken as negative.

(iv) Distances measured perpendicular to and above the principal axis (along + y-axis) are taken as positive.

(v) Distances measured perpendicular to and below the principal axis (along - y-axis) are taken as negative.

3. Refraction of Light:

(i) The phenomenon due to which a ray of light deviates from its path at the plane of the separation of two media, when the ray of light is travelling from one optical medium to another optical medium is called refraction of light.

(ii) The rays of light while travelling from rarer to denser medium bend towards the normal drawn at the point of incidence. The rays travelling from a denser to a rarer medium, bend away from the normal.

(iii) Refractive index of a medium, μ=Speed of light in vacuumSpeed of light in the medium.

(iv) Relative refractive index of medium 2 with respect to medium 1, μ2,1=Speed of light in medium 1Speed of light in medium 2.

(v) In a rectangular glass slab, when light is passing through two opposite faces, angle of incidence is always equal to that angle of the emergence.

4. Refraction by Spherical Lenses:

(i) Lens is a transparent medium bounded by two surfaces in which, one or both surfaces are spherical.

(ii) Convex lens is a lens which is thicker at the centre and thinner at its end.

(iii) Concave lens is a lens which is thinner at the centre and thicker at its end.

(iv) The centre point of a lens is known as its optical centre.

(v) The centre of the two imaginary spheres of which the lens is a part is known as centre of curvature of lens.

(vi) The radii of the two imaginary spheres of which the lens is a part are called radii of curvature of lens.

(vii) The imaginary line joining the two centres of curvature is called principal axis of lens.

(viii) The distance between focus and optical centre of a lens is known as focal length of lens.

(ix) The plane passing through the focus and perpendicular to the principal axis is known as focal plane.

(x) The effective diameter of the circular outline of a spherical lens is known as aperture of lens.

(xi) An imaginary axis, passing through the optical centre and perpendicular to the principal axis of the lens is called refractive axis.

(xii) The converging and diverging action of lenses can be explained by considering a lens made up of large number of different small angled prisms.

(xiii) A convex lens can form real/virtual, inverted/erect and diminished/magnified images depending on the position of object.

(xiv) A concave lens always form virtual, erect and diminished image.

5. Lens Formula and magnification:

(i) Lens formula for spherical lens is 1v-1u=1f and gives relationship between object distance u, image distance v and the focal length f.

(ii) Magnification produced by a lens, m=vu.

(iii) Power of lens P is the reciprocal of its focal length f in metre. The SI unit of power of a lens is dioptre (D). P=1fin metre.

The focal length of a convex lens is 25 cm. At what distance from the optical centre of the lens an object be placed to obtain a virtual image of twice the size?

Given,

Focal length, f = +25 cm

Image is virtual and magnified, m = +2

For a lens, magnification is

m = v / u

∴ +2 = v / u

∴ v = 2u

Lens formula is,

1 / v – 1 / u = 1 / f

∴ 1 / 2u – 1 / u = 1 / 25

∴ – 1 / 2u = 1 / 25

∴ 2u = – 25

∴ u = – 12.5 cm

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The focal length of a convex lens is 25 cm. At what distance from the optical centre of the lens an object be placed to obtain a virtual image of twice the size?

Focal length, f = +25 cm

Image is virtual and magnified, m = +2

For a lens, magnification is

m = `"v"/"u"`

`therefore + 2 = "v"/"u"`

∴ v = 2u

Lens formula is,

`1/"v" = 1/"u" = 1/"f"`

`therefore 1/"2u" - 1/"u" = 1/25`

`therefore -1/"2u" = 1/25`

∴ 2u = -25 cm

∴ u = -12.5 cm