Question

A ray of light traveling through air strikes a piece of diamond at an angle of incidence equal to 56 degrees. Calculate the angular separation in degrees between the red light and the violet light in the refracted ray, given that: The index of refraction of violet light ( Lamdaviolet = 400nm) in diamond is 2.46. The index of refraction of red light ( Lamdared = 700nm) in diamond is 2.41. Enter the numeric value in degrees.

Answer 1

The angle of separation is
`\Delta \theta = 0.93 ^o`

Step-by-step explanation:

From the question we are told that

The angle of incidence is
`\theta _ i = 56^o`

The refractive index of violet light in diamond is
`n_v = 2.46`

The refractive index of red light in diamond is
`n_r = 2.41`

The wavelength of violet light is
`\lambda _v = 400nm = 400*10^(-9)m`

The wavelength of red light is
`\lambda _r = 700nm = 700*10^(-9)m`

Snell's Law can be represented mathematically as

`(sin \theta_i)/(sin \theta_r) = n`

Where
`\theta_r` is the angle of refraction

=>
`sin \theta_r = (sin \theta_i)/(n)`

Now considering violet light

`sin \theta_r__(v)} = (sin \theta_i)/(n_v)`

substituting values

`sin \theta_r__(v)} = (sin (56))/(2.46)`

`sin \theta_r__(v)} = 0.337`

`\theta_r__(v)} = sin ^(-1) (0.337)`

`\theta_r__(v)} = 19.69^o`

Now considering red light

`sin \theta_r__(R)} = (sin \theta_i)/(n_r)`

substituting values

`sin \theta_r__(R)} = (sin (56))/(2.41)`

`sin \theta_r__(R)} = 0.344`

`\theta_r__(R)} = sin ^(-1) (0.344)`

`\theta_r__(R)} = 20.12^o`

The angle of separation between the red light and the violet light is mathematically evaluated as

`\Delta \theta = \theta_r__(R)} - \theta_r__(V)}`

substituting values

`\Delta \theta =20.12 - 19.69`

`\Delta \theta = 0.93 ^o`