Consider the original double-slit pattern from problem 1, shown below. Suppose that a third slit of the same width were added halfway between the original two slits as shown in the figure below the pattern. (Note that this results in the distance between adjacent slits becoming half of the original value.) Pattern on screen with two slits X Y Z Magnified view of slits Added slit d/2d/2- a. Would point Z be a principal maximum, a minimum, or neither? Explain your reasoning. b. Would point Y be a principal maximum, a minimum, or neither? Explain your reasoning. c. Would point X be a principal maximum, a minimum, or neither? Explain your reasoning.

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**2. Transforming a Two-Slit Arrangement into a Three-Slit One**

Consider the original double-slit pattern from problem 1, shown below. Suppose that a third slit of the same width is added halfway between the original two slits as shown in the figure below the pattern. (Note that this results in the distance between adjacent slits becoming half of the original value.)

**Pattern on screen with two slits:**

- The upper part of the diagram shows a typical interference pattern with bands of alternating light and dark regions labeled as X, Y, Z, and C.

**Magnified view of slits:**

- The lower part displays a magnified view of the slits. 
- The original distance \(d\) between slits is now divided into two equal parts, \(d/2\), due to the added slit. The added slit is marked clearly between the original two slits.

**Questions:**

a. Would point **Z** be a principal maximum, a minimum, or neither? Explain your reasoning.

b. Would point **Y** be a principal maximum, a minimum, or neither? Explain your reasoning.

c. Would point **X** be a principal maximum, a minimum, or neither? Explain your reasoning.
Transcribed Image Text:**2. Transforming a Two-Slit Arrangement into a Three-Slit One** Consider the original double-slit pattern from problem 1, shown below. Suppose that a third slit of the same width is added halfway between the original two slits as shown in the figure below the pattern. (Note that this results in the distance between adjacent slits becoming half of the original value.) **Pattern on screen with two slits:** - The upper part of the diagram shows a typical interference pattern with bands of alternating light and dark regions labeled as X, Y, Z, and C. **Magnified view of slits:** - The lower part displays a magnified view of the slits. - The original distance \(d\) between slits is now divided into two equal parts, \(d/2\), due to the added slit. The added slit is marked clearly between the original two slits. **Questions:** a. Would point **Z** be a principal maximum, a minimum, or neither? Explain your reasoning. b. Would point **Y** be a principal maximum, a minimum, or neither? Explain your reasoning. c. Would point **X** be a principal maximum, a minimum, or neither? Explain your reasoning.
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