Combination of Lenses

Effective Focal Length of Two Lenses in Contact: When two lenses with focal lengths f₁​ and f₂​ are placed in contact, the combined focal length f is given by:

\[\frac{1}{f}=\frac{1}{f_1}+\frac{1}{f_2}\]

This formula helps in determining the overall focusing ability of multiple lenses used together.

Effective Power of Combined Lenses: If the powers of the individual lenses are P₁​ and P₂​, then the total power P of the combination is: P=P₁+P₂​

This means that the power of the combined lens system is the sum of the individual powers.

Key Observations:

• If both lenses are convex (positive power): The combination results in a stronger converging effect.
• If both lenses are concave (negative power): The combination results in a stronger diverging effect.
• If one lens is convex and the other is concave: The total power depends on which has a greater magnitude.

Applications:

1. It is used in microscopes, telescopes, cameras, and corrective eyeglasses.
2. Helps in designing optical instruments by adjusting focal lengths and power for required magnification.