Assertion (A) Analysis: Laser Photon Properties

The assertion states that in lasers, emitted photons possess the same energy and phase as incident photons. This is a fundamental characteristic of laser light, primarily due to the process of stimulated emission. In stimulated emission, an incoming photon triggers an excited atom to release a second photon that is identical in energy (frequency/wavelength) and phase (coherent) to the incident photon. Therefore, Assertion (A) is true.

Reason (R) Analysis: Photon Amplitude and Brightness

The reason posits that the addition of individual photon amplitudes results in brighter light. Laser light is known for its high intensity or brightness. This brightness arises because the photons emitted are coherent (in phase) and monochromatic (same energy). When coherent waves overlap, they interfere constructively. The summation of their amplitudes leads to a significantly higher resultant amplitude, which corresponds to increased intensity or brightness (Intensity $\propto$ Amplitude$^2$). Thus, Reason (R) is also true.

Relationship Between Assertion (A) and Reason (R)

While both the assertion and the reason are factually correct statements about lasers:

• Assertion (A) describes the properties of individual emitted photons concerning the stimulating photons (identity in energy and phase).
• Reason (R) explains the collective effect of many such coherent photons leading to high brightness.

Reason (R) explains the consequence (brightness) resulting from the properties mentioned in Assertion (A) and the large number of photons generated. It does not explain the underlying mechanism *why* the emitted photons are identical in energy and phase to the incident ones; that mechanism is stimulated emission itself. Therefore, Reason (R) is not the correct explanation for Assertion (A).

Conclusion

Both Assertion (A) and Reason (R) are true statements, but Reason (R) does not provide the correct explanation for Assertion (A).