A ray of light passes through two 5 mm thick parallel glass slabs composed of different types of glass. The two slabs are separated by an 8 mm wide air gap. The index of refraction of the first slab is 1.55 while the index of the second is 1.48. The ray’s angle of incidence on the first slab of glass is 15 degrees. What is the angle of incidence of the ray on the second glass slab?

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .