Ray Optics and Optical Instruments

sin i / sin r = n₂₁ (constant), The incident ray, refracted ray and normal lie in the same plane, n₁₂ = 1/n₂₁

Snell's law states that the ratio of sine of angle of incidence to sine of angle of refraction is constant (refractive index). All three rays lie in the same plane. The refractive index is independent of angle of incidence and refraction occurs in both directions.

True

According to the Cartesian sign convention, focal length is positive for converging lenses (convex) and negative for diverging lenses (concave). Convex lenses converge parallel rays to a real focus.

Optical fibres, Totally reflecting prisms, Mirage formation, Diamond's brilliance

Total internal reflection is used in optical fibres for signal transmission, in prisms to bend light, in mirage formation due to temperature gradients, and gives diamond its brilliance. Rainbow formation involves dispersion, not total internal reflection.

Virtual and inverted

In a compound microscope, the objective forms a real, inverted, magnified image. The eyepiece then forms a virtual, magnified image of this first image. Since there are two inversions (one by objective, but eyepiece maintains the inverted nature), the final image is virtual and inverted.