Angle of deviation for light passing from glass prism is minimum for

Figure 1. Deviation of a light beam by a prism of angle at vertex A and refractive index n. A prism of angle at the apex A and index n – the air, of unit index, surrounds the prism – deflects a light beam, whose angle of incidence on one of the lateral surfaces of the prism is i, according to the laws of Snell-Descartes of geometric optics: sin i = n sin r and n sin r’ = sin i’ (Figure 1 for the notations). The angle of deflection D = i + i’– A, with A = r + r’. The light beam can only emerge from the prism if A <2 a sin(1/n) ; for ice n = 1.31, hence A < 99.5⁰. If we trace the deviation D as a function of i, we see that it decreases rapidly, reaches a minimum minimorum corresponding to a symmetrical crossing of the prism (i = i’), then increases slowly. The minimum is very flattened, so that a change in the angle of incidence around the incidence that corresponds to this minimum does not significantly change its value; it results in an accumulation of light and therefore a high luminosity around this minimum. For A = 60⁰, the minimum is 22⁰; if A = 90⁰, it is 46⁰ (Figure 2). Figure 3 shows the value of this minimum for the different values of A allowed: it increases with A. Figure 2. Deviation D as a function of the angle of incidence i on a prism of angle A = 60⁰ and angle A = 90⁰. Figure 3. Minimum deviation Dm as a function of the angle A of a prism. Figure 4. Deviation D for an angle prism A = 60⁰ depending on the colour of the incident light. Each of the four curves ...

The deviation of light occurs when a beam of light changes route as it travels from one medium to another. Refraction occurs twice when a ray of light passes through a prism. It enters and exits the prism twice. Light rays bend towards the normal while passing from an optically rarer media to an optically denser one. Light rays bend away from the typical direction when they move from an optically denser to an optically rarer material. The angle of deviation is defined as the angle formed by the incident and emerging rays. Prism A transparent optical device with flat, polished surfaces designed to refract light is known as an optical prism. Objects having two parallel surfaces are not prisms, as they must have at least one angled surface. Prisms can be created out of any material that is transparent to the wavelengths they are intended for. Glass, acrylic and fluorite are common materials. Types of Prisms • Dispersive Prism Because the refractive index of light varies with frequency, dispersive prisms are used to separate light into its constituent spectral colours. White light entering the prism is a combination of frequencies, each of which bends somewhat differently. Because blue light is slower than red light, it bends more. • Reflective Prism To flip, invert, spin, divert or displace the light beam, reflective prisms are employed to reflect it. Without the prisms, the image would be upside down for the user in binoculars or single-lens reflex cameras. • Beam-splitting ...

I attempt to explain the presence of a minimum mathematically instead of experimentally. The light ray travels through air and hits the glass prism, at an angle $\theta_1$ (the angle of incidence) to When the ray is in the glass, the angle of the ray changes to $\theta_2$ (the angle of refraction), to the normal of the glass boundary. The two angles are related by Snell's Law, such that: $$\frac - cosA\bigg) * sin\theta_1\Bigg)$$ Because I'm not good at math, this is where my analysis ends, and WolframAlpha begins. Punching in arbitrary values for the angle of prism, and for refractive indeces, The very fact that WolframAlpha can find minima for $\theta_1 + \theta_4$ means that there are values of $\theta_1$ such that $angle\space of\space deviation$ has minima. Notice that the values of the minimum are offset from the value of $\theta$ by a constant amount every time. I would like to answer this question step by step. Let's start from angle of deviation. Why do we need a measure called angle of deviation? It's because a ray of light undergo deviation from its actual path if it is allowed to pass from one medium to a different medium. This is due to the change in index of refraction of the media. The angle of deviation is a measure of how much this deviation has happened at the interface. In the case of a prism (usually made of glass), light enters the prism from air. Since air and prism have different refractive indices, light undergo a deviation from it's actual path. Le...

In the below figure (1), ABC represents the principal section of a glass-prism having ∠A as its refracting angle. A ray KL is an incident on the face AB at the point F where N1LO is the normal and ∠i1 is the angle of incidence. Since the refraction takes place from air to glass, therefore, the refracted ray LM bends toward the normal such that ∠r1 is the angle of refraction. If µ be the refractive index of glass with respect to air, then µ = s i n i s i n r (By Snell’s law) ∠QPN gives the angle of deviation ‘δ Thus, δ = i 1 – r 1 + i 2 − r 2….... (1) δ = i 1 + i 2 – ( r 1 + r 2 ) Again, in quadrilateral ALOM, ∠ALO + ∠AMO = 2 right angles [Since, ∠ALO = ∠AMO = 90º] So, ∠LAM +∠LOM = 2 right angles [Since, Sum of four angles of a quadrilateral = 4 right angles] ….... (2) Also in △ LOM, ∠ r 1 + ∠ r 2+ ∠LOM = 2 right angles …... (3) Comparing (2) and (3), we get ∠LAM = ∠ r 1 + ∠ r 2 A = ∠ r 1 + ∠ r 2 Using this value of ∠A, equation (1) becomes, δ = i 1 + i 2 − A