Step 1: Find the position equations for the fringes.
The position of the
nth bright fringe is given by:
yn=‌So, for the 5th bright fringe:
y5=‌The position of the
nth dark fringe is:
yn=‌For the 7 th dark fringe:
y7=‌=‌Step 2: Use the given distance between 5th bright and 7th dark fringes.
Distance between the 7th dark and 5th bright fringe:
y7−y5=‌−‌First, make the denominators the same:
‌−‌=‌The distance given in the question is
3mm:‌=3×10−3mStep 3: Find the value of
‌.
Divide both sides by 3:
‌=1×10−3 Now multiply both sides by 2 :
‌=2×10−3m So,
‌=2mmStep 4: Find the positions needed for the second distance.
Position of the 7th bright fringe:
y7′=‌Position of the 5th dark fringe:
y5′=‌=‌Step 5: Calculate the distance between 5th dark and 7th bright fringes.
y7′−y5′=‌−‌ Make denominators the same:
‌−‌=‌Step 6: Find the final answer using the value from earlier.
From (i),
‌=2mm, so:
‌=‌×2mm=5mmFinal Answer: Distance between 5th dark and 7th bright fringes is
5mm.