The refractive index n of transparent acrylic plastic (full name Poly(methyl methacrylate)) depends on the color (wavelength) of the light passing through it. At wavelength 486.1 nm (blue, designated with letter F) -> nF=1.497, and at wavelength 656.3 nm (red, designated with letter C) -> nC=1.488. Two beams (one of each wavelength) are prepared to coincide, and enter the flat polished surface of an acrylic block at angle of 45 arc degree measured from the normal to the surface. What is the angle between the blue beam and the red beam in the acrylic block?

The angle between the blue beam and the red beam in the acrylic block is  

Explanation:

From the question we are told that

     The  refractive index of the transparent acrylic plastic for blue light is  

     The  wavelength of the blue light is

    The  refractive index of the transparent acrylic plastic for red light is  

       The  wavelength of the red light is

    The incidence angle is  

Generally from Snell's law the angle of refraction of the blue light  in the acrylic block  is mathematically represented as

Where   is the refractive index of air which have a value of

So

Generally from Snell's law the angle of refraction of the red light in the acrylic block is mathematically represented as

Where   is the refractive index of air which have a value of

So

The angle between the blue beam and the red beam in the acrylic block

substituting values

a electromagnetic waves