Let vi be the velocity of light in air and vz the velocity of light in water. According to Fermať's Principle, a ray of light will travel from a point A in the air to a point B in the water by a path ACI that minimizes the time taken. Show that sin 61 sin 02 V2 where 0, (the angle of incidence) and 02 (the angle of refraction) are as shown. This equation is known as Snell's Law.
Let vi be the velocity of light in air and vz the velocity of light in water. According to Fermať's Principle, a ray of light will travel from a point A in the air to a point B in the water by a path ACI that minimizes the time taken. Show that sin 61 sin 02 V2 where 0, (the angle of incidence) and 02 (the angle of refraction) are as shown. This equation is known as Snell's Law.
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![### Snell's Law and Light Refraction
Let \( v_1 \) be the velocity of light in air and \( v_2 \) the velocity of light in water. According to Fermat's Principle, a ray of light will travel from a point \( A \) in the air to a point \( B \) in the water by a path \( ACB \) that minimizes the time taken. Show that:
\[ \frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} \]
where \( \theta_1 \) (the angle of incidence) and \( \theta_2 \) (the angle of refraction) are as shown. This equation is known as Snell’s Law.
#### Explanation of the Diagram:
The diagram shows a light ray traveling from point \( A \) above the water surface, bending at point \( C \) as it enters the water, and reaching point \( B \) underwater.
- **\( \theta_1 \)** is the angle of incidence, which is the angle between the incoming light ray (above water) and the normal line at the point of incidence \( C \).
- **\( \theta_2 \)** is the angle of refraction, which is the angle between the refracted light ray (under water) and the normal line at the point of refraction \( C \).
- The light ray follows the path \( ACB \), adjusting its direction at \( C \) to minimize the time taken according to Fermat's Principle.
The velocities \( v_1 \) (in air) and \( v_2 \) (in water) dictate the relationship between \( \theta_1 \) and \( \theta_2 \) as described by Snell's Law.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F28092663-10ce-474b-a101-95a46deb92bf%2F7fa9d95c-158f-47f1-9643-9b8d5e9f42a9%2Fqcy21qd.png&w=3840&q=75)
Transcribed Image Text:### Snell's Law and Light Refraction
Let \( v_1 \) be the velocity of light in air and \( v_2 \) the velocity of light in water. According to Fermat's Principle, a ray of light will travel from a point \( A \) in the air to a point \( B \) in the water by a path \( ACB \) that minimizes the time taken. Show that:
\[ \frac{\sin \theta_1}{\sin \theta_2} = \frac{v_1}{v_2} \]
where \( \theta_1 \) (the angle of incidence) and \( \theta_2 \) (the angle of refraction) are as shown. This equation is known as Snell’s Law.
#### Explanation of the Diagram:
The diagram shows a light ray traveling from point \( A \) above the water surface, bending at point \( C \) as it enters the water, and reaching point \( B \) underwater.
- **\( \theta_1 \)** is the angle of incidence, which is the angle between the incoming light ray (above water) and the normal line at the point of incidence \( C \).
- **\( \theta_2 \)** is the angle of refraction, which is the angle between the refracted light ray (under water) and the normal line at the point of refraction \( C \).
- The light ray follows the path \( ACB \), adjusting its direction at \( C \) to minimize the time taken according to Fermat's Principle.
The velocities \( v_1 \) (in air) and \( v_2 \) (in water) dictate the relationship between \( \theta_1 \) and \( \theta_2 \) as described by Snell's Law.
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