### The-Mirror-Equation-Ray-Optics-And-Optical-Instruments-By-Prof-M-R-Shenoy

### Key Concepts:

#### 1. The Mirror Equation:

- The mirror equation for spherical mirrors: $$(\frac{1}{f} = \frac{1}{v} + \frac{1}{u}),$$ where:
- (f) is the focal length of the mirror.
- (v) is the image distance (positive for real images, negative for virtual).
- (u) is the object distance (positive for real objects, negative for virtual).

#### 2. Sign Conventions:

- Understanding the sign conventions for distances:
- Positive distances are measured in the direction of the incident light.
- Negative distances are measured in the direction opposite to the incident light.
- Focal length ((f)) is positive for concave mirrors and negative for convex mirrors.

#### 3. Real vs. Virtual Images:

- Real images are formed when light rays converge and can be projected onto a screen.
- Virtual images are formed when light rays appear to diverge and cannot be projected.

#### 4. Magnification ((M)):

- Magnification ((M)) is a measure of how much the image is enlarged or reduced compared to the object.
- Magnification formula: $$(M = -\frac{v}{u}).$$
- Negative (M) indicates inversion (upside-down image), while positive (M) indicates an upright image.

#### 5. Ray Diagrams:

- Ray diagrams help visualize the path of light rays and the formation of images by mirrors.
- Rays typically drawn include:
- A ray parallel to the principal axis that reflects through the focal point for concave mirrors.
- A ray that passes through the focal point before reflecting parallel to the principal axis for concave mirrors.
- A ray directed towards the center of curvature that reflects back on itself.

### Formulas to Remember:

#### 1. The Mirror Equation:

- $$(\frac{1}{f} = \frac{1}{v} + \frac{1}{u})$$

#### 2. Magnification ((M)):

- $$(M = -\frac{v}{u})$$

### Mirror Configurations:

#### 1. Object Beyond Center of Curvature ((C)):

- Image is real, inverted, and located between the focus ((F)) and the center of curvature ((C)).

#### 2. Object at Center of Curvature ((C)):

- Image is real, inverted, and located at (C).

#### 3. Object Between (C) and (F):

- Image is real, inverted, and located beyond (C).

#### 4. Object at Focus ((F)):

- No real image is formed. Only virtual rays diverge.

#### 5. Object Between Mirror and Focus ((F)):

- Image is virtual, erect, and located on the same side as the object.