Light - Reflection and Refraction | Class 10 CBSE | Web Notes | Part 9: Lens Formula & Magnification, Power of Lenses

Lens Formula and Magnification

The lens formula gives the relationship between object distance (u), image distance (v), and the focal length (f). The lens formula is expressed as:

The lens formula is general and is valid in all situations for any spherical lens.
The magnification (m) produced by a lens is the ratio of the height of the image (h') to the height of the object (h).

Magnification is also related to the object distance (u) and the image distance (v).
Magnification m = h'/h = v/u.

A concave lens has a focal length of 15 cm. At what distance should the object from the lens be placed so that it forms an image at 10 cm from the lens? Also, find the magnification produced by the lens.

A concave lens always forms a virtual, erect image on the same side of the object.
Image distance v = –10 cm
Focal length f = –15 cm
Object distance u = ?

The positive sign shows that the image is erect and virtual. The image is one-third of the size of the object.

A 2.0 cm tall object is placed perpendicular to the principal axis of a convex lens of focal length 10 cm. The distance of the object from the lens is 15 cm. Find the nature, position, and size of the image. Also find its magnification.

or, v = +30 cm
The positive sign of v shows that the image is formed at a distance of 30 cm on the other side of the optical centre. The image is real and inverted.

The negative signs of m and h' show that the image is inverted and real. It is formed below the principal axis. Thus, a real, inverted image, 4 cm tall, is formed at a distance of 30 cm on the other side of the lens. The image is two times enlarged.

The ability of a lens to converge or diverge light rays depends on its focal length.
A convex lens of short focal length bends the light rays through large angles and focuses closer to the optical centre.
A concave lens of very short focal length causes higher divergence than one with a longer focal length.
The degree of convergence or divergence of light rays by a lens is expressed as its power.
The power of a lens (P) is defined as the reciprocal of its focal length (f).

The SI unit of power of a lens is dioptre (D).
1 dioptre is the power of a lens whose focal length is 1 metre (1D = 1m^–1).
The power of a convex lens is positive and that of a concave lens is negative.
Opticians prescribe corrective lenses indicating their powers. It is more convenient to use powers instead of focal lengths.
- A lens of power +2.0 D has a focal length of +0.50 m. The lens is convex.
- A lens of power –2.5 D has a focal length of –0.40 m. The lens is concave.
In many optical instruments, several lenses are combined to increase magnification and sharpness of the image. The net power (P) of the lenses placed in contact is the algebraic sum of the individual powers P₁, P₂, P₃, … (P = P₁ + P₂ + P₃ + …).
During eye-testing, an optician puts several corrective lenses of known power inside the testing spectacles’ frame. Thus, the required power of the lens is calculated by algebraic addition. E.g., two lenses of power +2.0 D and +0.25 D are equivalent to a single lens of power +2.25 D.
The simple additive property of the powers of lenses can be used to design lens systems to minimise certain defects in images produced by a single lens. Such a lens system is commonly used in the design of lenses for cameras, microscopes, and telescopes.

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