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]
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°.
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