Question

If two sources emit light waves of different amplitudes then

• A. brightness of fringes is less.
• B. fringes disappear after short time.
• C. fringe width is less.
• D. there is some intensity of light in the region of destructive interference.

Hint:

Remember that unequal amplitudes lower the overall contrast of an optical pattern but do not change its geometric spacing! The fringe width formula ($\beta = \frac{\lambda D}{d}$) depends only on wavelength and layout dimensions, so it remains completely unchanged.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
The question asks us to identify the optical consequence that occurs in an interference pattern when the two interfering light sources produce waves with unequal peak amplitudes ($a_1 \neq a_2$).

Step 2: Key Formula or Approach:
The resultant light intensities at the points of constructive (maximum) and destructive (minimum) interference are governed by the amplitude values: $$I_{\text{max}} \propto (a_1 + a_2)^2$$ $$I_{\text{min}} \propto (a_1 - a_2)^2$$ We analyze these relations to determine the physical state of the dark and bright bands on the screen.

Step 3: Detailed Explanation:
In an ideal double-slit interference configuration where both sources emit waves with identical amplitudes ($a_1 = a_2 = a$), the minimum intensity at a dark fringe drops perfectly to zero: $$I_{\text{min}} \propto (a - a)^2 = 0$$ This perfect cancellation creates completely dark bands, resulting in an interference pattern with ideal contrast. However, if the two sources have different amplitudes ($a_1 \neq a_2$), the subtraction in the minimum intensity formula will no longer yield zero: $$I_{\text{min}} \propto (a_1 - a_2)^2 \gt 0$$ This means that the cancellation at the points of destructive interference is incomplete. As a result, the "dark" fringes will still have a non-zero residual light intensity and appear faint or grey instead of completely black. This matches statement (D).

Step 4: Final Answer:
The correct consequence is that there is some intensity of light in the region of destructive interference, which corresponds to option (D).