### Shortcut Methods

#**Numerical Examples for Refraction Through a Prism and Dispersion:**

**Refractive Index**

- Refractive index of glass for red light: 1.52
- Refractive index of glass for blue light: 1.54

**Angle of Prism** - Angle of prism: 60 degrees
- Angle of prism: 45 degrees

**Angle of Deviation** - Angle of minimum deviation for red light: 40 degrees
- Angle of minimum deviation for blue light: 45 degrees

**Dispersion of Light** - Dispersive power of a prism: 0.02 (for visible spectrum)

**Critical Angle** - Critical angle for glass-air interface: 42 degrees

**Total Internal Reflection** - Condition for total internal reflection: i > c, where i is the angle of incidence and c is the critical angle

**Lens Formula** - Focal length of a convex lens: 20 cm
- Focal length of a concave lens: -15 cm

**Power of a Lens** - Power of a lens: 2 D (for a 50 cm focal length lens)

**Thin Lens Equation** - Object distance: 20 cm
- Image distance: 40 cm
- Focal length of the lens: 15 cm (using the thin lens equation 1/f = 1/u + 1/v)

**Magnification** - Magnification of a simple microscope: 10x
- Magnification of a compound microscope: 1000x

**Ray Diagrams** - Ray diagrams illustrating the refraction of light through a prism and the dispersion of light.
- Ray diagrams showing the formation of images by lenses, both converging and diverging.