Chapter 37, Problem 1OQ

(a)

To determine

The change you see when you gradually move the light source towards the central mirror, through a distance $\lambda /2$.

Answer to Problem 1OQ

Option (a), There is no change in the pattern.

Explanation of Solution

If the mirrors are not moved, the character of the interference system remains the same. This ensures no change in the pattern of the interference.

Conclusion:

Since there is no change in the pattern, option (a) is the correct answer.

Since the dark circle change into bright circle, option (b) is incorrect.

Since the dark circle changes into bright circle and then back into dark circle, option (c) is incorrect.

Since the dark circle changes into bright circle and then back into dark circle and then into bright circle, option (d) is incorrect.

(b)

To determine

The change you see when you gradually move the movable mirror towards the central mirror, through a distance $\lambda /2$.

Answer to Problem 1OQ

Option (c), The dark circle changes into a bright circle and then back into a dark circle.

Explanation of Solution

The mirrors are moved, so the character of the interference system will change. This ensures change in the pattern of the interference. The initial dark circle is due to the destructive interference pattern out of phase by $180°$.

The mirror is moved by $\lambda /2$ which changes the path difference by $2\left(\lambda /2\right)=\lambda$. This makes the waves to go in phase and out of phase to the original state.

Conclusion:

Since there is no change in the pattern, option (a) is the incorrect answer.

Since the dark circle changes into bright circle, option (b) is incorrect.

Since the dark circle changes into bright circle and then back into dark circle, option (c) is correct.

Since the dark circle changes into bright circle and then back into dark circle and then into bright circle, option (d) is incorrect.