Optics (Ray Optics and Wave Optics) - Important Derivations - Class XII

Here are the list of important derivations for Class XII Physics Chapters Ray Optics and Wave Optics. These two chapters constitute about 14 marks and a good amount of that goes to derivations. I used these derivations for my board exam revision and it was quite effective!
This Post deals about these derivations -

1. Derive the mirror formula for concave mirror
2. Show that Refractive Index = Real Depth / Apparent Depth
3. Derive a relation between critical angle and refractive index of a medium
4. Obtain the lens formula for a thin convex lens when the image is real
5. Two thin convex lenses of focal lengths f1 and f2 are kept in contact with each other coaxially. Deduce and expression for the effective focal length of the combination
6. Deduce and expression for the dispersive power of a prism.