Respuesta :
Answer:
a. The refractive index ranges from 1.5 - 1.56
b. 18.7° for violet light and 19.5° for red light.
c. 33.7° for violet light and 35.3° for red light.
Explanation:
a. The refractive index of an object is the ratio of the speed of light in a vacuum and the speed of light in the object.
Mathematically,
[tex]n = \frac{c}{v}[/tex]
The speed of violet light in the object is [tex]1.9 * 10^8 m/s[/tex].
The speed of red light in the object is [tex]2 * 10^8 m/s[/tex]
Hence, the refractive index for violet light is:
[tex]n = \frac{3 * 10^8 }{1.9 * 10^8} \\\\n = 1.56[/tex]
and for red light, it is:
[tex]n = \frac{3 * 10^8 }{2 * 10^8} \\\\n = 1.5[/tex]
Hence, the refractive index ranges from 1.5 - 1.56.
b. The refractive index is also the ratio of the sine of the angle of incidence to the sine of the angle of refraction.
[tex]n = \frac{sin(i)}{sin(r)}[/tex]
The angle of incidence is 30°.
The angle of refraction for violet light will be:
[tex]1.56 = \frac{sin(30)}{sin(r)}\\ \\sin(r) = \frac{sin(30)}{1.56} = \frac{0.5}{1.56} \\\\sin(r) = 0.3205\\\\r = 18.7^o[/tex]
And the angle of refraction for red light will be:
[tex]1.5 = \frac{sin(30)}{sin(r)}\\ \\sin(r) = \frac{sin(30)}{1.5} = \frac{0.5}{1.5} \\\\sin(r) = 0.3333\\\\r = 19.5^o[/tex]
The angle of refraction for red light is larger than that of violet light when the angle of incidence is 30°.
c. The angle of incidence is 60°.
The angle of refraction for violet light will be:
[tex]1.56 = \frac{sin(60)}{sin(r)}\\ \\sin(r) = \frac{sin(60)}{1.56} = \frac{0.8660}{1.56} \\\\sin(r) = 0.5551\\\\r = 33.7^o[/tex]
And the angle of refraction for red light will be:
[tex]1.5 = \frac{sin(60)}{sin(r)}\\ \\sin(r) = \frac{sin(60)}{1.5} = \frac{0.8660}{1.5} \\\\sin(r) = 0.5773\\\\r = 35.3^o[/tex]
The angle of refraction for red light is still larger than that of violet light when the angle of incidence is 60°.
