Answer:
The diagram you've provided seems to illustrate the refraction of light as it passes from air into glass, and it shows two angles: a 30-degree angle of incidence (where the light enters the glass) and a 60-degree angle of refraction (where the light travels within the glass).
The refractive index [tex]\( n \)[/tex] of a material can be calculated using Snell's law, which is stated as:
[tex]\[ n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \][/tex]
where:
- [tex]\( n_1 \)[/tex] is the refractive index of the first medium (air in this case, which is approximately 1 since the refractive index of air is very close to that of a vacuum),
- [tex]\( \theta_1 \)[/tex] is the angle of incidence,
- [tex]\( n_2 \)[/tex] is the refractive index of the second medium (glass in this case, which we are trying to find), and
- [tex]\( \theta_2 \)[/tex] is the angle of refraction.
To solve for the refractive index of glass [tex](\( n_2 \))[/tex], we rearrange the formula:
[tex]\[ n_2 = \frac{n_1 \sin(\theta_1)}{\sin(\theta_2)} \][/tex]
Given that [tex]\( n_1 \)[/tex] is approximately 1, [tex]\( \theta_1 = 60^\circ \)[/tex], and [tex]\( \theta_2 = 30^\circ \)[/tex], we can substitute these values into the formula to find [tex]\( n_2 \)[/tex]:
[tex]\[ n_2 = \frac{1 \times \sin(60^\circ)}{\sin(30^\circ)} \][/tex]
Now let's calculate this value.
The refractive index [tex]\( n_2 \)[/tex] of the glass, calculated using Snell's law with the given angles of incidence and refraction, is approximately 1.732. This value is a typical refractive index for common types of glass.
Explanation:
