Answered

The index of refraction for crown glass is 1.512 at a wavelength of 660 nm (red), whereas its index of refraction is 1.530 at a wavelength of 410 nm (violet). If both wavelengths are incident on a slab of crown glass at the same angle of incidence, 73.2°, what is the angle of refraction for each wavelength? (Enter your answers to at least two decimal places.)

Answer :

Answer:[tex]39.27^{\circ},38.72^{\circ}[/tex]

Explanation:

Given

Refractive index for red[tex]\left ( \mu \right )=1.512 [/tex]

Refractive index for violet[tex]\left ( \mu \right )=1.530[/tex]

Using snells law

[tex]n_1Sin\theta _1=n_2Sin\theta _2[/tex]

here [tex]n_1=1[/tex] for air

[tex]\theta _1=73.2^{\circ}[/tex]

[tex]1\times sin\left ( 73.2\right )=1.512sin\left ( \theta _2\right )[/tex]

[tex]sin\left ( \theta _2\right )=0.633[/tex]

[tex]\theta _2=39.27^{\circ}[/tex]

For Violet Light

[tex]n_1Sin\theta _1=n_3Sin\theta _3[/tex]

[tex]1\times sin\left ( 73.2\right )=1.530sin\left ( \theta _3\right )[/tex]

[tex]sin\left ( \theta _3\right )=0.6256[/tex]

[tex]\theta _3=38.72^{\circ}[/tex]

Lanuel

The angle of refraction for each wavelength are 39.27° and 38.72° respectively.

Given the following data:

Refractive index of crown glass = 1.512.

Refractive index of violet = 1.530.

Angle of incidence = 73.2°

What is Snell's law?

Snell's law gives the relationship between the angle of incidence and angle of refraction with respect to light or other waves that are passing through a media or two different substances such as glass, water, cladding, or air.

Snell's Law states that the when light or other waves travels from one medium to another, it generally refracts. Mathematically, it is given by this formula:

[tex]n_1sin \theta_1 = n_2sin \theta_2\\\\1sin 73.2 = 1.512sin \theta_2\\\\0.9573 =1.512sin \theta_2\\\\sin \theta_2 =\frac{0.9573}{1.512} \\\\\theta_2= sin^{-1}(0.6331)\\\\[/tex]

Angle 2 = 39.27°.

For the violet wave:

[tex]n_1sin \theta_1 = n_3sin \theta_3\\\\1sin 73.2 = 1.530sin \theta_3\\\\0.9573 =1.530sin \theta_3\\\\sin \theta_3 =\frac{0.9573}{1.530} \\\\\theta_3= sin^{-1}(0.6256)\\\\[/tex]

Angle 3 = 38.72°.

Read more on refraction here: https://brainly.com/question/15838784

Other Questions