prove that nsini=constant

plz show me solution

If we had any idea what n, and i was, we might be able to help.

n is refractive index, i is angle of incidence

To prove that nsinθ = constant, we need to determine the relationship between the variables n, θ, and the constant value.

One way to approach proving this equation is by using the Snell's law, which describes the relationship between the angles of incidence and refraction when light travels from one medium to another. It states:

n1sinθ1 = n2sinθ2

Where:
n1 and n2 are the refractive indices of the respective media, and
θ1 and θ2 are the angles of incidence and refraction, respectively.

To prove nsinθ = constant, we can consider a case where light is passing through a single medium. In this case, both the angles of incidence and refraction would be equal, as the light does not change medium. Therefore, we can set n1 = n2 = n (the refractive index of the single medium), and θ1 = θ2 = θ.

By substituting these values into Snell's law, we get:

n*sinθ = n*sinθ

As both sides of the equation are equal, we can conclude that nsinθ is indeed a constant value.

Alternatively, we can also prove this equation using trigonometric identities. By using the identity sin(2θ) = 2sinθcosθ, we can rewrite nsinθ as:

nsinθ = (2n/2) * sinθ = n(2sinθcosθ)/(2cosθ) = n(sin2θ)/(cosθ)

Since sin2θ and cosθ are both trigonometric functions and therefore constants, we can conclude that nsinθ is also a constant.

Thus, we have proven that nsinθ = constant.