Question

The missing order in a double slit diffraction pattern occurs when
• Slit width equal slit separation
• The condition for interference maxima and diffraction minima coincide
• The wavelength is very small
• The screen is too far

• A. Slit width equal slit separation
• B. The condition for interference maxima and diffraction minima coincide
• C. The wavelength is very small
• D. The screen is too far

Hint:

Missing order occurs when: \[ \boxed{ \text{Bright interference fringe overlaps diffraction minimum} } \] At diffraction minima, intensity becomes zero.

Answer 1

The Correct Option is B

Concept: In Young's double slit experiment with finite slit width:
• Interference pattern is produced due to two coherent sources.
• Diffraction envelope is produced due to finite slit width. Sometimes an interference maximum disappears because it coincides with a diffraction minimum. This phenomenon is called: \[ \boxed{ \text{Missing order} } \]

Step 1: Write the condition for interference maxima. In YDSE, bright fringes occur at: :contentReference[oaicite:0]{index=0} where:
• \(d\) = slit separation
• \(n\) = order of bright fringe

Step 2: Write the condition for diffraction minima. Diffraction minima occur at: :contentReference[oaicite:1]{index=1} where:
• \(a\) = slit width
• \(m\) = order of diffraction minimum

Step 3: Understand missing order condition. A missing order occurs when:
• An interference maximum falls exactly at the position of a diffraction minimum. At diffraction minima:
• Intensity becomes zero. Thus the corresponding interference bright fringe disappears. Hence: \[ \boxed{ \text{Interference maxima coincide with diffraction minima} } \]

Step 4: Analyze the options carefully. Option 1: “Slit width equal slit separation” This is not the general condition for missing order. Hence incorrect. Option 2: “The condition for interference maxima and diffraction minima coincide” This is exactly the correct condition. Hence Option 2 is correct. Option 3: “The wavelength is very small” Wavelength size alone does not create missing orders. Hence incorrect. Option 4: “The screen is too far” Screen distance affects fringe spacing but not missing order condition. Hence incorrect.

Step 5: Choose the correct answer. Therefore the correct answer is: \[ \boxed{ \text{The condition for interference maxima and diffraction minima coincide} } \] Hence the correct option is: \[ \boxed{(2)} \] Additional Understanding: Missing order occurs when: \[ \frac{d}{a}=n \] for some integer value. Then a bright interference fringe disappears. Final Conclusion: Missing order occurs when: \[ \boxed{ \text{Interference maxima coincide with diffraction minima} } \] Hence, the correct answer is: \[ \boxed{(2)} \]