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refractive index(n) = \(\frac{sin i}{sinr}\) where r = 180-(90+i) → r=90-i since sin(90-i)=cos i : refractive index(n) = \(\frac{sin i}{cos i}\) → tan i

Sin c = (1)/n = (1)/1.51 = 0.6622 ∴ c = sin-\(^1\) 0.6622 = 41.47

Real depth and apparent dept is due to refraction

Magnifications = V/U = 4 ∴ V = 4U 1/V + 1/U = 1/f 1/4u + 1/U = 1/12 5/4U = 1/12 4U = 12 x 5 = 60 ∴ U = 15 cm

the power of a lens is defined as the reciprocal of the focal length ,expressed in metre.Mathematically, the power of a lens in dioptres is given by:(1)/f(in cm). thus for lens of power of 4.0 dioptres we have that: (1)/(f) = +4.0 f= (1)/(4.0) = 0.25cm

critical angle formula = \(sin^{-1}\) \(\frac{n_2}{n_1}\) → \(sin^{-1}\) \(\frac{1}{1.33}\) = \(sin^{-1}\) 0.7518 = 48.75º

violet color will deviate the most. Red light shows the least amount of deviation

Total internal reflection (TIR) is the optical phenomenon in which waves arrive at the interface (boundary) from one medium to another (e.g., from water to air). that is from a more optically denser medium to a less optically denser medium.

This is called dispersion . A beam of white light passes through a prism and changes into a spectrum of colours. The spectrum is a band of seven colours which is obtained by splitting of white light by a glass prism. The order of colours from the lower end of spectrum is violet (V), indigo (I), blue (B), green (G), yellow (Y), orange (O), and red (R).

\( \theta _3 \) shows the angle of deviation

When the object is placed inside the focal point (u < f), the image is: → Virtual (formed on the same side as the object) → Erect (upright) → Magnified (larger than the object)

When white light passes through a prism, it is refracted (bent) at different angles depending on the wavelength (or color) of the light. This is because different colors of light travel at different speeds in the glass, leading to varying degrees of refraction. This phenomenon is known as dispersion.