Shortcut Methods
Shortcut Methods and Tricks to Solve Numericals on Power of a Lens and Combination of Thin Lenses in Contact:
1. Power of a Single Lens:
 For a thin lens, P= 1/f, where P is power in diopters and f is the focal length in meters.
 For a convex lens, f is positive, so P is positive.
 For a concave lens, f is negative, so P is negative.
2. Combination of Thin Lenses in Contact:

When thin lenses are placed in contact, the power of the combination is given by:
P = P1 + P2 + P3 +…+ Pn

For lenses of the same sign (+ or ), their powers are simply added.

For lenses of opposite signs (+ and ), the powers are added, and the sign of the lens with the greater power is assigned to the combination.
3. Lens Equation:
 The thin lens equation is: 1/f = 1/u + 1/v
 Where f is the focal length of the lens, u is the object distance, and v is the image distance.
4. Magnification:
 The magnification of a lens is given by: M = v/u
 For a virtual image, magnification is negative.
 For a real image, magnification is positive.
5. Real and Virtual Images:
 A convex lens always forms a real image (except when the object is at the focal point).
 A concave lens always forms a virtual image.
6. Ray Diagrams:
 Ray diagrams are a graphical representation of how light rays interact with lenses.
 These diagrams are useful in visualizing image formation and understanding the behavior of lenses.
7. Applications of lenses:
 Lenses are crucial components in numerous optical devices, including:
 Eyeglasses
 Telescopes
 Microscopes
 Cameras
 Projectors
 Lasers
 Optical sensors
 Medical imaging devices
 Photography
 Cinematography