Question

An electromagnetic wave with frequency $5.70 \times 10^{14}$ propagates with a speed of $2.17 \times 10^8$ in a certain piece of glass. Find

(a) the wavelength of the wave in the glass;

(b) the wavelength of a wave of the same frequency propagating in air.

• A. (a) $0.401 \ \mu m$ (b) $0.546 \ \mu m$
• B. (a) $0.391 \ \mu m$ (b) $0.536 \ \mu m$
• C. (a) $0.381 \ \mu m$ (b) $0.526 \ \mu m$
• D. (a) $0.411 \ \mu m$ (b) $0.556 \ \mu m$

Answer 1

Answer: (C)

c. (a) $0.381 \ \mu m$ (b) $0.526 \ \mu m$

Answer 2

Concept:

The speed of an electromagnetic wave, its frequency, and wavelength are related by the equation $v = f\lambda$, where $v$ is the speed, $f$ is the frequency, and $\lambda$ is the wavelength. When an electromagnetic wave passes from one medium to another, its frequency ($f$) remains constant, while its speed ($v$) and wavelength ($\lambda$) change. The speed of light in air (or vacuum) is approximately $c = 3.00 \times 10^8$ m/s.

(a) Wavelength in glass:

Using the formula $\lambda_g = v_g/f$. Substitute given speed in glass ($2.17 \times 10^8$ m/s) and frequency ($5.70 \times 10^{14}$ Hz) to get $\lambda_g = 0.381 \times 10^{-6}$ m, which is $0.381 \ \mu m$.

(b) Wavelength in air:

Use the formula $\lambda_a = c/f$. Substitute speed of light in air ($3.00 \times 10^8$ m/s) and the same frequency ($5.70 \times 10^{14}$ Hz) to get $\lambda_a = 0.526 \times 10^{-6}$ m, which is $0.526 \ \mu m$.