If speed2 is greater than speed1, the transmission angle will be greater than the incident angle. Which choice best describes this relationship?

If speed2 is greater than speed1, the transmission angle will be greater than the incident angle. Which choice best describes this relationship?

• A. Cannot determine
• B. Greater than
• C. Equal to
• D. Less than

Answer: (B)

Snell’s law for waves ties the incident and transmitted angles to the speeds in the two media. It can be written as sin θi / sin θt = v1 / v2. If the speed in the second medium is greater than the speed in the first, then v1 / v2 is less than 1, so sin θt = (v2 / v1) sin θi. Since v2 / v1 is greater than 1, sin θt is larger than sin θi, and for angles between 0 and 90 degrees this means θt is larger than θi. Therefore the transmission angle is greater than the incident angle (as long as transmission is possible and not halted by total internal reflection).

Snell’s law for waves ties the incident and transmitted angles to the speeds in the two media. It can be written as sin θi / sin θt = v1 / v2. If the speed in the second medium is greater than the speed in the first, then v1 / v2 is less than 1, so sin θt = (v2 / v1) sin θi. Since v2 / v1 is greater than 1, sin θt is larger than sin θi, and for angles between 0 and 90 degrees this means θt is larger than θi. Therefore the transmission angle is greater than the incident angle (as long as transmission is possible and not halted by total internal reflection).