Question

When a photon enters glass from air, which one of the following quantities does not change?

• A. Velocity
• B. Wavelength
• C. Momentum
• D. Energy

Hint:

Always remember this core rule of wave optics: Frequency is a characteristic of the source, whereas Wavelength and Velocity are characteristics of the medium. Since energy depends solely on frequency, it never changes during refraction!

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The problem asks us to identify the physical property of a photon that remains completely invariant when it undergoes refraction, crossing the boundary interface from air into a solid glass medium.

Step 2: Key Formula or Approach:
The energy $E$ of an individual photon depends exclusively on Planck's constant $h$ and the monochromatic frequency $\nu$ of the radiation: $$E = h\nu$$ When a wave crosses from one medium into another, its frequency is determined solely by the source of emission and remains constant during propagation.

Step 3: Detailed Explanation:
When light enters an optically denser medium like glass, its speed $v$ decreases according to the medium's refractive index $n$ ($v = \frac{c}{n}$). Since the wave equation dictates $v = \nu\lambda$, a decrease in velocity while keeping the frequency $\nu$ constant causes a proportional contraction in the wavelength $\lambda$. Furthermore, since the de Broglie momentum of a photon is given by $p = \frac{h}{\lambda}$, the shift in wavelength directly alters its momentum. However, because the frequency $\nu$ is entirely independent of the refractive characteristics of the surrounding optical medium, the energy expression $E = h\nu$ remains perfectly unchanged.

Step 4: Final Answer:
The quantity that does not change is energy, which corresponds to option (D).