Magnifying Power:
Magnifying power refers to the ability of an optical instrument, such as a microscope or a telescope, to magnify the apparent size of an object. It is defined as the ratio of the angle subtended by the image formed by the instrument to the angle subtended by the object when viewed with the naked eye. The magnifying power is a measure of how much larger an object appears when viewed through the instrument compared to when viewed with the naked eye.

Angular Magnification:
Angular magnification, also known as angular amplification, is a measure of how much an optical instrument magnifies the angle subtended by an object. It is the ratio of the angle subtended by the image formed by the instrument to the angle subtended by the object itself. Angular magnification is commonly used in the context of telescopes and binoculars.

Linear Magnification:
Linear magnification, also known as lateral magnification, is a measure of how much an optical instrument magnifies the linear size of an object. It is the ratio of the size of the image formed by the instrument to the size of the object itself. Linear magnification is commonly used in the context of microscopes and magnifying glasses.

Differences:
The main differences between magnifying power, angular magnification, and linear magnification are as follows:

1. Definition:
- Magnifying Power: It is the ratio of the angle subtended by the image formed by the instrument to the angle subtended by the object when viewed with the naked eye.
- Angular Magnification: It is the ratio of the angle subtended by the image formed by the instrument to the angle subtended by the object itself.
- Linear Magnification: It is the ratio of the size of the image formed by the instrument to the size of the object itself.

2. Measurement:
- Magnifying Power: It is measured in terms of angular units (radians or degrees).
- Angular Magnification: It is measured in terms of the ratio of angles.
- Linear Magnification: It is measured as a dimensionless ratio or as a factor.

3. Application:
- Magnifying Power: It is commonly used in the context of telescopes and microscopes to determine the level of magnification they provide.
- Angular Magnification: It is commonly used in the context of telescopes and binoculars to quantify the degree of magnification in terms of angular size.
- Linear Magnification: It is commonly used in the context of microscopes, magnifying glasses, and cameras to determine the level of magnification in terms of linear size.

In summary, magnifying power, angular magnification, and linear magnification are different measures of the magnification capabilities of optical instruments. Magnifying power focuses on the angle subtended by the image compared to the object, angular magnification quantifies the magnification in terms of angles, and linear magnification measures the magnification in terms of linear size. Each measure has its own relevance and application in different optical instruments and scenarios.